From the UK link:
The Negotiated tender procedure is the most complicated. It is used if there are no tenders, or irregular or unacceptable tenders, in response to a call for tenders in the Official Journal, or, because of the specific nature of the goods or services required.

After having compared this with the wording in the Danish link I think the terms mean the same.

--------------------------------------------------
Note added at 19 hrs 26 mins (2003-11-10 16:12:08 GMT)
--------------------------------------------------

Sorry. Turns out that the Danish link was a bit too indirect. Here\'s the Danish wording I was talking about:

Udbud efter forhandling
Denne udbudsmetode tager hensyn til de særlige situationer, hvor man ikke kan få egnede tilbud ved at bruge offentligt eller begrænset udbud. Det er kun i de situationer, der er angivet i direktivet, at det er tilladt at bruge denne metode. Der sondres mellem udbud efter forhandling med og uden forudgående udbudsbekendtgørelse. Ved \"forudgående annoncering\" bekendtgør kommunen udbuddet og indleder derefter forhandling med tilbudsgiverne. Undlades den forudgående annoncering, henvender kommunen sig direkte til mulige leverandører efter eget valg og forhandler kontraktvilkårene med en eller flere af disse.

Regarding \"post tender negotiation\", here comes a definition of that term:

PTN is defined as: ‘negotiation after receipt of formal bids or tenders and before the letting of contract(s) with those companies submitting tender(s) offering the best value for money with a view to obtaining an improvement in content in circumstances which do not put the other tenderers at a disadvantage, distort competition or affect adversely trust in the competitive tendering process.
http://www.inlandrevenue.gov.uk/manuals/pummanual/procuremen...




--------------------------------------------------
Note added at 19 hrs 30 mins (2003-11-10 16:16:14 GMT)
--------------------------------------------------

Seems that \"post tender negotiation\" might be the same as \"udbud efter forhandling med forudgående udbudsbekendtgørelse\".