Around 60 academic and support staff at Swansea University may find themselves without jobs at the end of the year.
The university says external funding for 130 posts will stop with the end of European Union Objective One funding, but some 70 staff have been redeployed.
It said it was working to secure jobs for the remaining 60.
One union said the assembly government and EU could do more to co-ordinate the continuity of funding for those on fixed-term contracts.
A university spokesperson said: "A small proportion of university staff is employed on fixed-term contracts as a result of externally-funded projects - this is common practice across most UK universities.
"The end of the Objective 1 programme has however resulted in a number of posts terminating on 31 December.
"In June we identified up to 130 externally-funded academic and support staff that might be affected.
"In fact 70 of these have already been redeployed within the university or have their contracts renewed."
It said there was "well-developed and extensive consultation procedures" it was following that ensured staff coming to the end of their contracts were automatically informed of all new posts.
"The university is currently working to secure alternative funding for those remaining," added the spokesperson.
Andrew Morgan, president of Swansea's University and College Union, which represents academic, research and administrative staff, said to date the university had acted "with appropriate care" towards those affected.
"I would be hopeful that a very significant number of these will be resolved in an appropriate fashion but that does not stop anxiety amongst staff about potential job losses," he added.
"There are a fair number of staff at anyone time, especially research staff, on fixed term contracts."
He said the assembly government and EU needed to be better coordinated to stop short-term funding gaps.