CYPRESS CAPITAL PARTNERS I LP
SC 13G, 1997-01-24
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<PAGE>   1
                                UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549


                                SCHEDULE 13G


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

                                DYNAMEX INC.
                 -------------------------------------------
                              (Name of Issuer)

                        Common Stock, $.01 Par Value
         -----------------------------------------------------------
                       (Title of Class of Securities)

                                 26784F-10-3
                 -------------------------------------------
                               (CUSIP Number)


*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
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).
<PAGE>   2
CUSIP NO. 26784F-10-3                                                Page 2 of 5


                                SCHEDULE 13G



<TABLE>
================================================================================================================
<S>        <C>                                                                                      <C>
     1     Name of Reporting Person SS. or I.R.S. Identification No. of Above Person

                                            Cypress Capital Partners I, L.P.
- ----------------------------------------------------------------------------------------------------------------
     2     Check the Appropriate Box if a Member of a Group                                          (a) [ ]
                                                                                                     (b) [ ]
- ----------------------------------------------------------------------------------------------------------------

     3     SEC Use Only

- ----------------------------------------------------------------------------------------------------------------

     4     Citizenship or Place of Organization
                                                         Texas
- ----------------------------------------------------------------------------------------------------------------
                      5      Sole Voting Power
                                                                2,141,752
  Number of       ----------------------------------------------------------------------------------------------
  shares              6      Shared Voting Power
  beneficially                                                      0
  owned by        ----------------------------------------------------------------------------------------------
  each                7      Sole Dispositive Power
  reporting                                                     2,141,752
  person with     ----------------------------------------------------------------------------------------------
                      8      Shared Dispositive Power
                                                                    0
                  ----------------------------------------------------------------------------------------------
     9     Aggregate Amount Beneficially Owned by Each Reporting Person

                                                       2,141,752
- ----------------------------------------------------------------------------------------------------------------

    10     Check Box if the Aggregate Amount in Row (9) Excludes Certain Shares                          [ ]

- ----------------------------------------------------------------------------------------------------------------

    11     Percent of Class Represented by Amount in Row (9)

                                                         31.9%
- ----------------------------------------------------------------------------------------------------------------

    12     Type of Reporting Person
                                                           PN
================================================================================================================
</TABLE>

                      SEE INSTRUCTIONS BEFORE FILLING OUT!
<PAGE>   3
CUSIP NO. 26784F-10-3                                                Page 3 of 5

                                   ITEM 1(a)

Name of Issuer: Dynamex Inc.

                                   ITEM 1(b)

Address of Issuer's Principal Executive Offices:  2630 Skymark Avenue, Suite 610
                                                  Mississauga, Ontario L4W 5A4

                                   ITEM 2(a)

Name of Person Filing: Cypress Capital Partners I, L.P.

                                   ITEM 2(b)

Address of Principal Business Office or, of none, Residence: 13355 Noel Road, 
                                                             Suite 1050
                                                             Dallas, Texas 75240

                                   ITEM 2(c)

Citizenship: Texas

                                   ITEM 2(d)

Title of Class of Securities: Common Stock, $.01 par value

                                   ITEM 2(e)

CUSIP Number: 26784F 10 3

                                     ITEM 3

If this statement is filed pursuant to Rules 13d-1(b), or 13d-2(b), check
whether the person filing 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)   [ ] Investment Adviser registered under section 203 of the 
                   Investment Advisers Act of 1940
         (f)   [ ] Employee Benefit Plan, Pension Fund which is subject to 
                   the provisions of the Employee Retirement Income Security 
                   Act of 1974 or Endowment Fund; see Section 
                   240.13d-1(b)(1)(ii)(F)
         (g)   [ ] Parent Holding Company, in accordance with Section 
                   240.13d-1(b)(ii)(G) (Note: See Item 7)
         (h)   [ ] Group, in accordance with Section 240.13d-1(b)(1)(ii)(H)
<PAGE>   4
CUSIP NO. 26784F-10-3                                                Page 4 of 5

                                     ITEM 4

Ownership.

         (a)   Amount Beneficially Owned: 2,141,752

         (b)   Percent of Class:         31.9%

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

               (i)     sole power to vote or to direct the vote 2,141,752
               (ii)    shared power to vote or to direct the vote
               (iii)   sole power to dispose or to direct the disposition of
                       2,141,752
               (iv)    shared power to dispose or to direct the disposition of

                                     ITEM 5

Ownership of Five Percent or Less of a Class.

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

                                     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.
<PAGE>   5
CUSIP NO. 26784F-10-3                                                Page 5 of 5


         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.

Date:    January 16, 1997

Signature:       CYPRESS CAPITAL PARTNERS I, L.P.

                 By: CCP Investment Corporation, its general partner


                          By: /s/ THOMAS L. HARRISON
                              -----------------------------------
                              Thomas L. Harrison, President


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