<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934


                             NATIONAL-OILWELL, INC.
                                (Name of Issuer)

                     COMMON STOCK, par value $.01 per share
                         (Title of Class of Securities)

                                  637071-10-1
                                 (CUSIP Number)








<PAGE>   2



CUSIP No.  637071-10-1

<TABLE>
<S>                                                                                 <C>
1)       Name of Reporting Person                                                       DPI Oil Service Partners
                                                                                        Limited Partnership
         S.S. or I.R.S. Identification No.  of Above Person

2)       Check the appropriate box if a member of a Group                               (a)X
                                                                                        (b)N/A

3)       SEC Use Only

4)       Citizenship or place of organization                                           U.S.A.

Number of Shares           (5)      Sole Voting Power                                   0
Beneficially Owned         (6)      Shared Voting Power                                 4,725,281
by Each Reporting          (7)      Sole Dispositive Power                              0
Person with                (8)      Shared Dispositive Power                            4,725,281

9)       Aggregate Amount Beneficially  Owned by
         Each Reporting Person                                                          4,725,281

10)      Check Box if the Aggregate Amount in Row (9)
         Excludes certain Shares                                                        N/A

11)      Percent of Class Represented by Amount in Row 9                                27.4%

12)      Type of Reporting Person                                                       PN

</TABLE>




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CUSIP No.  637071-10-1

<TABLE>
<S>                                                                                  <C>
1)       Name of Reporting Person                                                       DPI Partners II
                                                                                        Limited Partnership
         S.S. or I.R.S. Identification No.  of Above Person

2)       Check the appropriate box if a member of a Group                               (a)X
                                                                                        (b)N/A

3)       SEC Use Only

4)       Citizenship or place of organization                                           U.S.A.

Number of Shares           (5)      Sole Voting Power                                   0
Beneficially Owned         (6)      Shared Voting Power                                 376,519
by Each Reporting          (7)      Sole Dispositive Power                              0
Person with                (8)      Shared Dispositive Power                            376,519

9)       Aggregate Amount Beneficially  Owned by
         Each Reporting Person                                                          376,519

10)      Check Box if the Aggregate Amount in Row (9)
         Excludes certain Shares                                                        N/A

11)      Percent of Class Represented by Amount in Row 9                                2.2%

12)      Type of Reporting Person                                                       PN

</TABLE>




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CUSIP No.  637071-10-1

<TABLE>
<S>                                                                                <C>
1)       Name of Reporting Person                                                       Inverness/Phoenix L.L.C.
         S.S. or I.R.S. Identification No.  of Above Person

2)       Check the appropriate box if a member of a Group                               (a)X
                                                                                        (b)N/A

3)       SEC Use Only

4)       Citizenship or place of organization                                           U.S.A.

Number of Shares           (5)      Sole Voting Power                                   0
Beneficially Owned         (6)      Shared Voting Power                                 5,101,800*
by Each Reporting          (7)      Sole Dispositive Power                              0
Person with                (8)      Shared Dispositive Power                            5,101,800*

9)       Aggregate Amount Beneficially  Owned by
         Each Reporting Person                                                          5,101,800

10)      Check Box if the Aggregate Amount in Row (9)
         Excludes certain Shares                                                        N/A

11)      Percent of Class Represented by Amount in Row 9                                29.6%

12) Type of Reporting Person                                                            CO 
 </TABLE>

*Represents shares directly owned by DPI Oil Service Partners Limited
Partnership and DPI Partners II Limited Partnership, of which Inverness/Phoenix
L.L.C. is, in each case, the managing general partner.



<PAGE>   5



CUSIP No.  637071-10-1

<TABLE>
<S>                                                                                 <C>
1)       Name of Reporting Person                                                       W. McComb Dunwoody
         S.S. or I.R.S. Identification No.  of Above Person

2)       Check the appropriate box if a member of a Group                               (a)X
                                                                                        (b)N/A

3)       SEC Use Only

4)       Citizenship or place of organization                                           U.S.A.

Number of Shares           (5)      Sole Voting Power                                   0
Beneficially Owned         (6)      Shared Voting Power                                 5,101,800*
by Each Reporting          (7)      Sole Dispositive Power                              0
Person with                (8)      Shared Dispositive Power                            5,101,800*

9)       Aggregate Amount Beneficially  Owned by
         Each Reporting Person                                                          5,101,800

10)      Check Box if the Aggregate Amount in Row (9)
         Excludes certain Shares                                                        N/A

11)      Percent of Class Represented by Amount in Row 9                                29.6%

12)      Type of Reporting Person                                                       IN
 </TABLE>

*Represents shares directly owned by DPI Oil Service Partners Limited
Partnership and DPI Partners II Limited Partnership, of which Inverness/Phoenix
L.L.C. is, in each case, the managing general partner. Mr. Dunwoody serves on
the investment committee of Inverness/Phoenix L.L.C. The investment committee
has sole power to vote and dispose of investments of Inverness/Phoenix L.L.C.



<PAGE>   6



CUSIP No.  637071-10-1

<TABLE>
<S>                                                                                  <C>
1)       Name of Reporting Person                                                       James C. Comis III
         S.S. or I.R.S. Identification No.  of Above Person

2)       Check the appropriate box if a member of a Group                               (a)X
                                                                                        (b)N/A

3)       SEC Use Only

4)       Citizenship or place of organization                                           U.S.A.

Number of Shares           (5)      Sole Voting Power                                   0
Beneficially Owned         (6)      Shared Voting Power                                 5,101,800*
by Each Reporting          (7)      Sole Dispositive Power                              0
Person with                (8)      Shared Dispositive Power                            5,101,800*

9)       Aggregate Amount Beneficially  Owned by
         Each Reporting Person                                                          5,101,800

10)      Check Box if the Aggregate Amount in Row (9)
         Excludes certain Shares                                                        N/A

11)      Percent of Class Represented by Amount in Row 9                                29.6%

12)      Type of Reporting Person                                                       IN
 </TABLE>

*Represents shares directly owned by DPI Oil Service Partners Limited
Partnership and DPI Partners II Limited Partnership, of which Inverness/Phoenix
L.L.C. is, in each case, the managing general partner. Mr. Comis serves on the
investment committee of Inverness/Phoenix L.L.C. The investment committee has
sole power to vote and dispose of investments of Inverness/Phoenix L.L.C.



<PAGE>   7



                   SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS
                         FILED PURSUANT TO RULE 13d-1(c)

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 Persons Filing:
             DPI Oil Service Partners Limited Partnership
             DPI Partners II Limited Partnership
             Inverness/Phoenix L.L.C.
             W. McComb Dunwoody
             James C. Comis III

Item 2(b).   Address of Principal Business Office or, if None, Residence:
             660 Steamboat Road
             Greenwich, CT 06830

Item 2(c).   Citizenship:
             U.S.A.

Item 2(d).   Title of Class of Securities:
             Common Stock, par value $.01 per share

Item 2(e).   CUSIP Number:
             637071-10-1

Item 3.      This statement is filed pursuant to Rule 13d-1(c).

Item 4.      Ownership
             (a)      Amount Beneficially Owned:  5,101,800
             (b)      Percent of Class:  29.6%
             (c)      Number of shares as to which such persons have:
                 (i)   sole power to vote or to direct the vote:  0
                 (ii)  shared power to vote or to direct the vote: 5,101,800
                 (iii) sole power to dispose or to direct the disposition of: 0
                 (iv)  shared power to dispose or to direct the disposition 
                       of: 5,101,800

Item 5.      Ownership of Five Percent or Less of a Class.
             Not applicable.

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



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             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.
             See attached Exhibit A

Item 9.      Notice of Dissolution of Group.
             Not applicable.

Item 10.     Certification.
             Not applicable (statement is filed pursuant to Rule 13d-1(c)).




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                                    SIGNATURE

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

                                                Dated: February 11, 1997



                                  \s\ W. McComb Dunwoody
                                  --------------------------------------------
                                  DPI Oil Service Partners Limited Partnership
                                  By Inverness/Phoenix L.L.C. its managing
                                  general partner
                                  By its President


                                  \s\ W. McComb Dunwoody
                                  --------------------------------------------
                                  DPI Partners II Limited Partnership
                                  By Inverness/Phoenix L.L.C. its managing
                                  general partner
                                  By its President

                                  \s\ W. McComb Dunwoody
                                  --------------------------------------------
                                  Inverness/Phoenix L.L.C.
                                  By its President



                                  \s\ W. McComb Dunwoody
                                  --------------------------------------------
                                  W. McComb Dunwoody


                                  \s\ James C. Comis III
                                  --------------------------------------------
                                  James C. Comis III




<PAGE>   10


EXHIBIT A

                       IDENTIFICATION OF MEMBERS OF GROUP

Pursuant to Item 8 of Schedule 13G, this exhibit identifies the persons who
have filed this Schedule 13G as members of a group:

Name:    DPI Oil Service Partners Limited Partnership
Address:          660 Steamboat Road
                  Greenwich, CT 06830
Name:    DPI Partners II Limited Partnership
Address:          660 Steamboat Road
                  Greenwich, CT 06830
Name:    Inverness/Phoenix L.L.C.
Address:          660 Steamboat Road
                  Greenwich, CT 06830
Name:  W. McComb Dunwoody
Address:          660 Steamboat Road
                  Greenwich, CT 06830
Name:  James C. Comis
Address:          660 Steamboat Road
                  Greenwich, CT 06830