<PAGE>
 
                                                                    Exhibit 10.2

                      SIXTH AMENDMENT TO CREDIT AGREEMENT
                      -----------------------------------

     SIXTH AMENDMENT TO CREDIT AGREEMENT (this "Amendment"), dated as of April
30, 1998, among DADE BEHRING HOLDINGS, INC. ("Holdings"), DADE BEHRING INC. (the
"Borrower"), the financial institutions party to the Credit Agreement referred
to below (the "Banks") and BANKERS TRUST COMPANY, as Agent (the "Agent") for the
Banks.  All capitalized terms used herein and not otherwise defined shall have
the respective meanings provided such terms in the Credit Agreement.

                              W I T N E S S E T H:
                              - - - - - - - - - - 

     WHEREAS, Holdings, the Borrower, the Banks and the Agent are parties to a
Credit Agreement, dated as of May 7, 1996 and amended and restated as of April
29, 1997 (as amended, modified, restated or supplemented to the date hereof, the
"Credit Agreement"); and

     WHEREAS, the parties hereto wish to amend the Credit Agreement as herein
provided;

     NOW, THEREFORE, it is agreed:

I.  Amendments to Credit Agreement.
    ------------------------------ 

          1.   Section 10 of the Credit Agreement is hereby amended by deleting
the date "April 30, 1998" appearing in the definitions of "Applicable Base Rate
Margin" and "Applicable Eurodollar Margin" and by inserting in lieu thereof the
date "October 31, 1998."

II.  Miscellaneous Provisions.
     ------------------------ 

          1.   In order to induce the Banks to enter into this Amendment, the
Borrower hereby represents and warrants that:

          (a) no Default or Event of Default exists as of the Sixth Amendment
     Effective Date, both before and after giving effect to this Amendment; and

          (b) all of the representations and warranties contained in the Credit
     Agreement or the other Credit Documents are true and correct in all
     material respects on and as of the Sixth Amendment Effective Date, both
     before and after giving effect to this Amendment, with the same effect as
     though such representations and warranties had been made on and as of the
     Sixth Amendment Effective Date (it being understood that any representation
     or warranty made as of a specific date shall be true and correct in all
     material respects as of such specific date).
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          2.   This Amendment is limited as specified and shall not constitute a
modification, acceptance or waiver of any other provision of the Credit
Agreement or any other Credit Document.

          3.   This Amendment may be executed in any number of counterparts and
by the different parties hereto on separate counterparts, each of which
counterparts when executed and delivered shall be an original, but all of which
shall together constitute one and the same instrument.  A complete set of
counterparts shall be lodged with the Borrower and the Agent.

          4.   THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES
HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAW OF THE
STATE OF NEW YORK.

          5.   This Amendment shall become effective as of April 30, 1998 on the
date (the "Sixth Amendment Effective Date") when each of Holdings, the Borrower
and the Banks shall have signed a counterpart hereof (whether the same or
different counterparts) and shall have delivered (including by way of facsimile
transmission) the same to the Agent at its Notice Office.

          6.   From and after the Sixth Amendment Effective Date, all references
in the Credit Agreement and each of the other Credit Documents to the Credit
Agreement shall be deemed to be references to the Credit Agreement as amended
hereby.

                           *            *           *

                                      -2-
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          IN WITNESS WHEREOF, the parties hereto have caused their duly
authorized officers to execute and deliver this Amendment as of the date first
above written.

                                     DADE BEHRING HOLDINGS, INC.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Nancy A. Krejsa
                                     Title: Vice President & Treasurer
 
 
                                     DADE BEHRING INC.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Nancy A. Krejsa
                                     Title: Vice President & Treasurer
 
 
                                     BANKERS TRUST COMPANY,
                                     Individually, as Agent
                                     and as Collateral Agent
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Anthony LoGrippo
                                     Title: Vice President
 
 
                                     THE BANK OF NOVA SCOTIA
 
 
                                     By/s/
                                       --------------------------------------   
                                     Name:  F.C.H. Ashby
                                     Title: Senior Manager Loan Operations
 
 
                                     BANK OF TOKYO-MITSUBISHI
                                     TRUST COMPANY
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Paul P. Malecki
                                     Title: Vice President

                                      -3-
<PAGE>
 
                                     BANKBOSTON, N.A.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Marie C. Duprey
                                     Title  Vice President
 
 
                                     GENERAL ELECTRIC CAPITAL
                                     CORPORATION
 
 
                                     By: /s/
                                        ---------------------------------------
                                     Name:  Holly Kaczmarczyk
                                     Title: Duly Authorized Signatory
 
 
                                     SANWA BUSINESS CREDIT
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Stanley Kaminski
                                     Title: Vice President
 
 
                                     ABN AMRO BANK N.V., Chicago Branch
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  John E. Robertson
                                     Title: Vice President
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Bernard J. McGulgan
                                     Title: Group Vice President & Director
 
 
                                     CREDIT AGRICOLE INDOSUEZ
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  David Bouhl, F.V.P.
                                     Title: Head of Corporate Banking Chicago
 
 

                                      -4-
<PAGE>
 
                                     By/s/
                                       ---------------------------------------  
                                     Name:  Katherine L. Abbott
                                     Title: First Vice President
 
 
                                     OCTAGON LOAN TRUST
                                     By: Octagon Credit Investors, its Manager
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  James P. Ferguson
                                     Title: Managing Director
 
 
                                     CITIBANK, N.A.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Steven Kaufman
                                     Title: Vice President
 
 
                                     CRESCENT/MACH I PARTNERS, L.P.
                                     By TCW Asset Management Company,
                                     its Investment Manager
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:
                                     Title:
 
 
                                     STRATA FUNDING LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  John H. Cullinane
                                     Title: Director
 
 
                                     CERES FINANCE LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name: John H. Cullinane        
                                     Title: Director

                                      -5-
<PAGE>
 
                                     AERIES FINANCE LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Andrew Ian Wignall
                                     Title: Director
 
 
                                     CAPTIVA FINANCE LTD.
 
 
                                     By/s/
                                       --------------------------------------- 
                                     Name:  John H. Cullinane
                                     Title:  Director
 
 
                                     CAPTIVA II FINANCE LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  John H. Culinane
                                     Title: Director
 
 
                                     CITY NATIONAL BANK
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Patrick M. Cassidy
                                     Title: Vice President
 
 
                                     ROYALTON COMPANY,
                                     By Pacific Investment Management Company
                                     as its Investment Advisor
                                     By:  PIMCO Management Inc., a general
                                          partner
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Richard M. Weil
                                     Title: Senior Vice President
 
 

                                      -6-
<PAGE>
 
                                     FIRST NATIONAL BANK OF CHICAGO
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Michael A. Basak
                                     Title: First Vice President
 
 
                                     FLOATING RATE PORTFOLIO
                                     By:  Chancellor LGT - Senior Secured
                                          Managment, Inc., as Attorney-in-Fact
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Anthony R. Clemente
                                     Title: Authorized Signatory
 
 
                                     KEYPORT LIFE INSURANCE COMPANY
                                     By:  Stein, Roe & Farnham, as Investment
                                          Advisor
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Brian G. Good
                                     Title: Vice President as Portfolio Manager
 
 
                                     DAI-ICHI KANGYO BANK LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Sunao Hirata
                                     Title: Vice President
 
 
                                     PRIME INCOME TRUST
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:
                                     Title:
 
 

                                      -7-
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                                     THE FUJI BANK, LIMITED
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Peter L. Chinnici
                                     Title: Joint General Manager
 
 
                                     MERRILL LYNCH
                                     SENIOR FLOATING RATE FUND, INC.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Gilles Marchand, CFA
                                     Title: Authorized Signatory
 
 
                                     ML CBO IV (CAYMAN) LTD.
                                     By Protective Asset Management Company
                                     as Collateral Manager
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  James Dondero CFA, CPA
                                     Title: President
                                            Protective Asset Management Company
 
 
                                     NORTHWESTERN MUTUAL LIFE
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:
                                     Title:
 
 
                                     PILGRIM AMERICA PRIME RATE TRUST
                                     By:  PILGRIM AMERICA INVESTMENTS,
                                          INC., as its Investment Manager
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Michael J. Bacevica
                                     Title: Vice President
 
 

                                      -8-
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                                     SAKURA BANK LTD.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Yukiharu Sakumoto
                                     Title: Joint General Manager
 
 
                                     SOCIETE GENERALE
 
 
                                     By/s/
                                       --------------------------------------- 
                                     Name:  John M. Stack
                                     Title: Director
 
 
                                     SOUTHERN PACIFIC BANK
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Chris Kelleher
                                     Title: Vice President
 
 
                                     VAN KAMPEN AMERICAN CAPITAL PRIME
                                     RATE INCOME TRUST
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Jeffrey W. Maillet
                                     Title: Senior Vice President & Director
 
 
                                     IMPERIAL BANK
 
 
                                     By/s/
                                       ---------------------------------------  
                                     Name:  Ray Vadalma
                                     Title: Senior Vice President
 
 
                                     MERRILL LYNCH PRIME RATE PORTFOLIO
                                     By:  Merrill Lynch Asset Management L.P.,
                                     as Investment Advisor
 
 

                                      -9-
<PAGE>
 
                                     By/s/
                                       --------------------------------------- 
                                     Name:  Gilles Marchand, CFA
                                     Title: Authorized Signatory
 
 
                                     SENIOR HIGH INCOME PORTFOLIO, INC.
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:
                                     Title:
 
 
                                     MERRILL LYNCH DEBT STRATEGIES
                                     PORTFOLIO
                                     By:  Merrill Lynch Asset Management L.P.,
                                          as Investment Advisor
 
 
                                     By/s/
                                       ---------------------------------------
                                     Name:  Gilles Marchand, CFA
                                     Title: Authorized Signatory
 
 
                                     AG CAPITAL FUNDING PARTNERS, L.P.
                                     By: Angelo, Gordon & Co., L.P., as
                                         Investment Advisor
 
 
                                     By/s/
                                       --------------------------------------- 
                                     Name:  Fred Berger
                                     Title: Chief Financial Officer

                                      -10-