<PAGE>
 
                                                                    Exhibit 10.1

                      FIFTH AMENDMENT TO CREDIT AGREEMENT
                      -----------------------------------

     FIFTH 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 4.02(A)(c) of the Credit Agreement is hereby amended by
adding at the end thereof the following new sentence:

     "Notwithstanding anything to the contrary contained above in this Section
     4.02(A)(c), only 75% of the Net Proceeds resulting from an Asset Sale
     permitted under Section 8.02(hh) shall be required to be applied as a
     mandatory repayment of Term Loans as provided above in this Section
     4.02(A)(c)."

          2.   Section 8.02 of the Credit Agreement is hereby amended by (i)
deleting the word "and" appearing at the end of clause (ff) thereof, (ii)
deleting the period at the end of clause (gg) thereof and inserting a semi-colon
in lieu thereof and (iii) inserting at the end thereof the following new clauses
(hh) and (ii):

               "(hh) the Borrower and/or its Subsidiary may sell their controls
     (TQC) business, provided that the Net Proceeds therefrom are either applied
                     --------                                                   
     to repay Term Loans as provided in Section 4.02(A)(c) or reinvested to the
     extent permitted by Section 4.02(A)(c); and

               (ii) the Borrower and/or its Subsidiaries may sell their desktop
     chemistry analyzer business."
<PAGE>
 
          3.   The definition of "Asset Sale" appearing in Section 10 of the
Credit Agreement is hereby amended by deleting the text "(cc) and (dd)"
appearing at the end thereof and inserting in lieu thereof the text "(cc), (dd)
and (ii)".

II.  Consents and Agreements.
     ----------------------- 

          1.   Notwithstanding anything to the contrary contained in Sections
7.11 and 8.16 of the Credit Agreement, in the Pledge Agreement, in the First
Amendment or in the Second Amendment, the Banks hereby agree that Holdings and
its Subsidiaries shall not be required to pledge to the Pledgee under the Pledge
Agreement the stock of any Foreign Subsidiary acquired pursuant to the Behring
Acquisition and required to be pledged pursuant to the terms of the Pledge
Agreement until October 31, 1998.

III. 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 Fifth 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 Fifth 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
     Fifth 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).

          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.

                                      -2-
<PAGE>
 
          5.   This Amendment shall become effective on the date (the "Fifth
Amendment Effective Date") when each of Holdings, the Borrower and the Required
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 Fifth 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 modified
hereby.

                           *            *           *

                                      -3-
<PAGE>
 
          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:  Mary Kay Coyle
                                       Title: Managing Director
 
 
                                       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

                                      -4-
<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

                                      -5-
<PAGE>
 
                                       By/s/
                                         -------------------------------------- 
                                       Name:  Katherine L. Abbott
                                       Title: First Vice President
 
 
                                       OCTAGON CREDIT INVESTORS LOAN
                                       PORTFOLIO, a Unit of The Chase
                                       Manhattan Bank
 
 
                                       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:  Justin L. Driscoll
                                       Title: Senior Vice President
 
 
                                       STRATA FUNDING LTD.
 
 
                                       By/s/
                                         ---------------------------------------
                                       Name:  John H. Cullinane
                                       Title: Director
 

                                      -6-
<PAGE>
 
                                       CERES FINANCE LTD.
 

                                       By/s/
                                         ---------------------------------------
                                       Name:  John H. Cullinane
                                       Title: Director
 
 
                                       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
 

                                      -7-
<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:
 

                                      -8-
<PAGE>
 
                                      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:  John E. Schlifske
                                      Title: Vice President
 
 
                                      PILGRIM AMERICA PRIME RATE TRUST
                                      By:  PILGRIM AMERICA INVESTMENTS,
                                           INC., as its Investment Manager
 
                                      By/s/
                                        ---------------------------------------
                                      Name:  Michael J. Bacevica
                                      Title: Vice President
 
 
                                      SAKURA BANK LTD.
 
 
                                      By/s/
                                        ---------------------------------------
                                      Name:  Yukiharu Sakumoto
                                      Title: Joint General Manager
 

                                      -9-
<PAGE>
 
                                      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
 
 
                                      By/s/
                                        ---------------------------------------
                                      Name:  Gilles Marchand, CFA
                                      Title: Authorized Signatory
 

                                      -10-
<PAGE>
 
                                      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

                                      -11-