<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, DC 20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 2)*

                              NATIONAL-OILWELL, INC.
- --------------------------------------------------------------------------------
                              (Name of Issuer)

                          Common Stock, $.01 par value
- --------------------------------------------------------------------------------
                       (Title of Class of Securities)

                                  637071 10 1
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

                                February 2, 1998
- --------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)

         Check the appropriate box to designate the rule pursuant to which this
Schedule is filed:

                  [ ]    Rule 13d-1(b)

                  [X]    Rule 13d-1(c)

                  [ ]    Rule 13d-1(d)

         *The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which would
alter the disclosures provided in a prior cover page.

         The information required on the remainder of this cover page shall not
be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act, but shall be subject to all other provisions of the Act (however, see
the Notes).

                        (Continued on following page(s))
                               Page 1 of 10 Pages

<PAGE>   2
                                                            

CUSIP NO. 637071 10 1                 13G                 PAGE  2   OF 10  PAGES
- --------------------------------------------------------------------------------
 (1)    Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
        (entities only)
        GENERAL ELECTRIC CAPITAL CORPORATION, a New York corporation
        I.R.S. Identification No. 13-1500700 
- --------------------------------------------------------------------------------
 (2)    Check the Appropriate Box if a Member of a Group     (a) [ ]
        (See Instructions)                                   (b) [X]

- --------------------------------------------------------------------------------
 (3)    SEC Use Only

- --------------------------------------------------------------------------------
 (4)    Citizenship or Place of Organization 
        New York, U.S.A.
- --------------------------------------------------------------------------------
    Number of              
                           (5)     Sole Voting Power                          
      Shares                       2,135,804
                           -----------------------------------------------------
   Beneficially            (6)     Shared Voting Power                        
                                   -0-                                          
     Owned by              -----------------------------------------------------
                           (7)     Sole Dispositive Power                     
       Each                        2,135,804
                           -----------------------------------------------------
     Reporting             (8)     Shared Dispositive Power                   

    Person With                    -0-
- --------------------------------------------------------------------------------
 (9)    Aggregate Amount Beneficially Owned by Each Reporting Person  
        2,135,804        
- --------------------------------------------------------------------------------
 (10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares 
        (See Instructions)  [ ]
- --------------------------------------------------------------------------------
 (11)   Percent of Class Represented by Amount in Row (9) 
        4.03%
- --------------------------------------------------------------------------------
 (12)   Type of Reporting Person (See Instructions)
        CO
- --------------------------------------------------------------------------------



<PAGE>   3
                                                            

CUSIP NO. 637071 10 1                 13G                 PAGE  3   OF 10  PAGES
- --------------------------------------------------------------------------------
  (1)   Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
        (entities only)
        GENERAL ELECTRIC CAPITAL SERVICES, INC., a Delaware corporation
        I.R.S. Identification No. 06-11095031
- --------------------------------------------------------------------------------
  (2)   Check the Appropriate Box if a Member of a Group     (a) [ ]
        (See Instructions)                                   (b) [X]

- --------------------------------------------------------------------------------
  (3)   SEC Use Only

- --------------------------------------------------------------------------------
  (4)   Citizenship or Place of Organization 
        Delaware, U.S.A.
- --------------------------------------------------------------------------------
    Number of              
                           (5)     Sole Voting Power                          
      Shares                       Disclaimed. See Item 9 Below.
                           -----------------------------------------------------
   Beneficially            (6)     Shared Voting Power                        
                                   -0-                                          
     Owned by              -----------------------------------------------------
                           (7)     Sole Dispositive Power                     
       Each                        Disclaimed. See Item 9 Below.
                           -----------------------------------------------------
     Reporting             (8)     Shared Dispositive Power                   

    Person With                    -0-
- --------------------------------------------------------------------------------
  (9)   Aggregate Amount Beneficially Owned by Each Reporting Person  
        Beneficial ownership is disclaimed by General Electric Capital 
        Services, Inc.
- --------------------------------------------------------------------------------
 (10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares 
        (See Instructions)  [ ]
- --------------------------------------------------------------------------------
 (11)   Percent of Class Represented by Amount in Row (9) 
        Not applicable. See Item 9 above.
- --------------------------------------------------------------------------------
 (12)   Type of Reporting Person (See Instructions)
        CO
- --------------------------------------------------------------------------------



<PAGE>   4
                                                            

CUSIP NO. 637071 10 1                 13G                 PAGE  4   OF 10  PAGES
- --------------------------------------------------------------------------------
  (1)   Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
        (entities only)
        GENERAL ELECTRIC COMPANY, a New York corporation 
        I.R.S. Identification No. 14-0089340 
- --------------------------------------------------------------------------------
  (2)   Check the Appropriate Box if a Member of a Group     (a) [ ]
        (See Instructions)                                   (b) [X]

- --------------------------------------------------------------------------------
  (3)   SEC Use Only

- --------------------------------------------------------------------------------
  (4)   Citizenship or Place of Organization 
        New York, U.S.A.
- --------------------------------------------------------------------------------
    Number of              
                           (5)     Sole Voting Power                          
      Shares                       Disclaimed. See Item 9 Below.
                           -----------------------------------------------------
   Beneficially            (6)     Shared Voting Power                        
                                   -0-                                          
     Owned by              -----------------------------------------------------
                           (7)     Sole Dispositive Power                     
       Each                        Disclaimed. See Item 9 Below.
                           -----------------------------------------------------
     Reporting             (8)     Shared Dispositive Power                   

    Person With                    -0-
- --------------------------------------------------------------------------------
  (9)   Aggregate Amount Beneficially Owned by Each Reporting Person  
        Beneficial ownership is disclaimed by General Electric Company.
- --------------------------------------------------------------------------------
 (10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares 
        (See Instructions)  [ ]
- --------------------------------------------------------------------------------
 (11)   Percent of Class Represented by Amount in Row (9) 
        Not applicable. See Item 9 above.
- --------------------------------------------------------------------------------
 (12)   Type of Reporting Person (See Instructions)
        CO
- --------------------------------------------------------------------------------



<PAGE>   5
CUSIP Number: 637071 10 1            13G                      Page 5 of 10 Pages


Item 1(a).        Name Of Issuer:

                  National-Oilwell, Inc.

Item 1(b).        Address of Issuer's Principal Executive Offices:

                  5555 San Felipe
                  Houston, Texas 77056

Item 2(a).        Name of Person Filing:

                  This statement is being filed by:

                  (i)   General Electric Capital Corporation, a New York
                        corporation ("GE Capital");

                  (ii)  General Electric Capital Services, Inc., a Delaware
                        corporation ("GECS"), which owns all of the outstanding
                        capital stock of GE Capital; and

                  (iii) General Electric Company, a New York corporation ("GE"),
                        which owns all of the outstanding capital stock of GECS.

Item 2(b).        Address of Principal Business Office:

                  (i)   GE Capital 
                        260 Long Ridge Road
                        Stamford, Connecticut 06927

                  (ii)  GECS 
                        260 Long Ridge Road 
                        Stamford, Connecticut 06927

                  (iii) GE 
                        3135 Easton Turnpike
                        Fairfield, Connecticut 06431

Item 2(c).        Citizenship:

                  New York, U.S.A.

Item 2(d).        Title of Class of Securities:

                  Common stock, $.01 par value (the "Common Stock").


<PAGE>   6


CUSIP Number: 637071 10 1            13G                      Page 6 of 10 Pages


Item 2(e).        CUSIP Number:

                  637071 10 1

Item  3.          If this statement is filed pursuant to Rules 13d-1(b), or 
                  13d-2(b) or (c), check whether filing person is a:

        (a) [ ] Broker or dealer registered under Section 15 of the Act 

        (b) [ ] Bank as defined in Section 3(a)(6) of the Act 

        (c) [ ] Insurance company as defined in Section 3(a)(19) of the Act 

        (d) [ ] Investment company registered under Section 8 of the Investment
                Company Act 

        (e) [ ] An investment adviser in accordance with Rule 13d-1(b)(1)(ii)(E)

        (f) [ ] An employee benefit plan or endowment fund in accordance with
                Rule 13d-1(b)(1)(ii)(F)

        (g) [ ] A parent holding company or control person in accordance with 
                Rule 13d-1(b)(ii)(G)

        (h) [ ] A savings association as defined in Section 3(b) of the Federal 
                Deposit Insurance Act (12 U.S.C. 1813)

        (i) [ ] A church plan that is excluded from the definition of an 
                investment company under Section 3(c)(14) of the Investment 
                Company Act of 1940 (15 U.S.C. 80a-3)

        (j) [ ] Group, in accordance with Rule 13d-1(b)(1)(ii)(J)

        If this statement is filed pursuant to Rule 13d-1(c), check this box.
        [X]

Item 4.  Ownership

         (a)      Amount Beneficially Owned:

                  As of December 31, 1998, GE Capital was the beneficial owner
                  of 2,135,804 shares of Common Stock (the "GE Capital Shares").
                  The GE Capital Shares constitute 4.03% of the outstanding
                  shares of Common Stock based on 52,996,785 shares of Common
                  Stock outstanding. GECS and GE disclaim beneficial ownership
                  in any shares of Common Stock.

         (b)      Percent of Class:

                  4.03%

         (c)      Number of shares as to which the person has:

                  (i)    sole power to vote or direct the vote:  2,135,804

                  (ii)   shared power to vote or direct the vote:  -0-



<PAGE>   7
CUSIP Number: 637071 10 1            13G                      Page 7 of 10 Pages

                  (iii)  sole power to dispose or to direct the disposition 
                         of:  2,135,804

                  (iv)   shared power to dispose or to direct the disposition 
                         of:  -0-

Item 5.  Ownership of Five Percent or Less of a Class.

         If this Schedule is being filed to report the fact that as of the date
         hereof the reporting person has ceased to be the beneficial owner of
         more than five percent on the class of securities, check the following
         box. [ X ]

Item 6.  Ownership of More than Five Percent on Behalf of Another Person.

         Not applicable.

Item 7.  Identification and Classification of the Subsidiary Which Acquired the
         Security Being Reported on by the Parent Holding Company.

         Not applicable.

Item 8.  Identification and Classification of Members of the Group.

         Not applicable.

Item 9.  Notice of Dissolution of Group.

         Not applicable.

Item 10. Certification.

         By signing below, General Electric Capital Corporation certifies that,
         to the best of its knowledge and belief, the securities referred to
         above were not acquired and are not held for the purpose of or with
         the effect of changing or influencing the control of the issuer of the
         securities and were not acquired and are not held in connection with
         or as a participant in any transaction having that purpose or effect.




<PAGE>   8
CUSIP Number: 637071 10 1            13G                      Page 8 of 10 Pages



                                    SIGNATURE


After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Statement is true, complete and correct.

                                           GENERAL ELECTRIC CAPITAL CORPORATION



                                            By:      /s/ Michael A. Gaudino
                                               ---------------------------------
                                                 Name:  Michael A. Gaudino
                                                 Title:    Vice President



                                            Dated:  February 12, 1999




<PAGE>   9

CUSIP Number: 637071 10 1            13G                      Page 9 of 10 Pages



                                    SIGNATURE


After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Statement is true, complete and correct.

                                         GENERAL ELECTRIC CAPITAL SERVICES, INC.



                                         By:      /s/ Michael A. Gaudino        
                                            ------------------------------------
                                             Name:  Michael A. Gaudino
                                             Title: Attorney-in-Fact




                                            Dated:  February 12, 1999



<PAGE>   10



CUSIP Number: 637071 10 1          13G                       Page 10 of 10 Pages


                                  SIGNATURE


After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Statement is true, complete and correct.

                                         GENERAL ELECTRIC COMPANY



                                         By:      /s/ Michael A. Gaudino        
                                            ------------------------------------
                                             Name:  Michael A. Gaudino
                                             Title: Attorney-in-Fact



                                         Dated:  February 12, 1999



<PAGE>   11
                                POWER OF ATTORNEY

The undersigned, General Electric Capital Services, Inc., a Delaware corporation
(hereinafter referred to as the "Corporation") does hereby make, constitute and
appoint the persons listed below as the Corporation's true and lawful agent and
attorney-in-fact (hereinafter referred to as the "Attorney") to act either
together or alone in the name and on behalf of the Corporation for and with
respect to the matters hereinafter described.

                  Name of Attorney:               Michael A. Gaudino
                                                  J. Gordon Smith
                                                  Michael E. Pralle
                                                  Paul J. Licursi

Each Attorney shall have the power and authority to do the following:

                  To execute and deliver any Schedule 13D, Schedule 13G or Forms
                  3, 4 and 5 or any amendments thereto required to be filed with
                  the Securities and Exchange Commission under the Securities
                  Exchange Act of 1934 on behalf of the Corporation with regard
                  to any securities owned by the Corporation, General Electric
                  Capital Corporation or any of their subsidiaries.

And, in connection with the foregoing, to execute and deliver all documents,
acknowledgments, consents and other agreements and to take such further action
as may be necessary or convenient for the Corporation in order to more
effectively carry out the intent and purpose of the foregoing.

Agreements, commitments, documents, instruments, and other writings executed by
the Attorney in accordance with the terms hereof shall be binding upon the
Corporation without attestation and without affixation of the seal of the
Corporation. The Power of Attorney conferred hereby shall not be delegable by
any Attorney. The Attorney shall serve without compensation for acting in the
capacity of agent and attorney-in-fact hereunder.

Unless revoked by the Corporation, this Power of Attorney shall be governed
under the laws of the State of New York and the authority of the Attorney
hereunder shall terminate on March 31, 2000.

IN WITNESS WHEREOF, the Corporation has caused this Power of Attorney to be
executed, attested and its corporate seal to be affixed pursuant to authority
granted by the Corporation's board of directors, as of the 30th day of April,
1998.

                                       GENERAL ELECTRIC CAPITAL SERVICES, INC.



         (Corporate Seal)
                                       By:      /s/ Nancy E. Barton
                                          -------------------------------------
                                          Nancy E. Barton, Senior Vice President

Attest:

         /s/ Brian T. McAnaney              
- ----------------------------------------
Brian T. McAnaney, Assistant Secretary



<PAGE>   12



                                POWER OF ATTORNEY

The undersigned, General Electric Company, a New York corporation (hereinafter  
referred to as the "Corporation") does hereby make, constitute and appoint the
persons listed below as the Corporation's true and lawful agent and
attorney-in-fact (hereinafter referred to as the "Attorney") to act either
together or alone in the name and on behalf of the Corporation for and with
respect to the matters hereinafter described.

                  Name of Attorney:                Joan C. Amble
                                                   Nancy E. Barton
                                                   Jeffrey S. Werner
                                                   Michael A. Gaudino
                                                   J. Gordon Smith
                                                   Michael E. Pralle
                                                   Paul J. Licursi

Each Attorney shall have the power and authority to do the following:

                  To execute and deliver any Schedule 13D, Schedule 13G or Forms
                  3, 4 and 5 or any amendments thereto required to be filed with
                  the Securities and Exchange Commission under the Securities
                  Exchange Act of 1934 on behalf of the Corporation with regard
                  to any securities owned by the Corporation, General Electric
                  Capital Corporation or any of their subsidiaries.

And, in connection with the foregoing, to execute and deliver all documents,
acknowledgments, consents and other agreements and to take such further action
as may be necessary or convenient for the Corporation in order to more
effectively carry out the intent and purpose of the foregoing.

Agreements, commitments, documents, instruments, and other writings executed by
the Attorney in accordance with the terms hereof shall be binding upon the
Corporation without attestation and without affixation of the seal of the
Corporation. The Power of Attorney conferred hereby shall not be delegable by
any Attorney. The Attorney shall serve without compensation for acting in the
capacity of agent and attorney-in-fact hereunder.

Unless revoked by the Corporation, this Power of Attorney shall be governed
under the laws of the State of New York and the authority of the Attorney
hereunder shall terminate on March 31, 2000.

IN WITNESS WHEREOF, the Corporation has caused this Power of Attorney to be
executed, attested and its corporate seal to be affixed pursuant to authority
granted by the Corporation's board of directors, as of the 30th day of April,
1998.

                                              GENERAL ELECTRIC COMPANY

         (Corporate Seal)
                                              By:   /s/ Philip D. Ameen
                                                 -------------------------------
                                                 Philip D. Ameen, Vice President
Attest:

         /s/ Robert E. Healing              
- --------------------------------------
Robert E. Healing, Attesting Secretary