Please efer to German to English translation of Negativerklärung, which I am sure is the exact equivalent of Danish negativerklæring:

http://chi.proz.com/kudoz/98792

Google search results are numerous.

Deutsche Bank | Negative clause-
Negative clause, Deutsche Bank. Also referred to as negative pledge. Obligation on the part of a debtor with respect to the creditor, in the case of long-term credits and bond issues, to refrain from encumbering specific assets ...
www.deutsche-bank.de/lexikon/2465.html

negative pledge clause Definition-
negative pledge clause - definition of negative pledge clause - A covenant in a bond agreement whereby the borrower agrees not to pledge any assets if such pledging would result in less security for the...
www.investorwords.com/3219/negative_pledge_clause.html

Negative Pledge - Reuters Financial Glossary-
Negative Pledge. From Reuters Financial Glossary. A clause in a bond agreement which prevents the borrower from pledging greater security or collateral to other lenders. ...
glossary.reuters.com/index.php/Negative_Pledge


--------------------------------------------------
Note added at 5 hrs (2007-08-03 17:40:09 GMT)
--------------------------------------------------

Judging from the google searches, it seems that "negative covenant/clause" is the broadest concept of those answers I offered:

Legal Definition of Covenant-
A negative covenant is one where the party binds himself that he has not performed and will not perform a certain act; ... There is also a difference between a negative covenant, which is only in affirmance of an affirmative covenant ...
www.lectlaw.com/def/c323.htm

http://law.jrank.org/pages/8778/Negative-Covenant.html

Forbes: Financial Glossary-
Negative covenant. A bond covenant that limits or prohibits altogether certain actions unless the bondholders agree. Sitemap Help Contact Us Investment Newsletters Forbes Conferences Forbes Magazines Forbes Autos Ad Information ...
www.forbes.com/tools/glossary/search.jhtml?term=negative_co...

If it involves a loan agreement, then negative pledge may be more accurate. It depends on the context, but "negative covenant" applies in all cases.