Last year, the PSNI launched a legal bid to gain access to interviews with former republicans and loyalists held by Boston College.
They are being sought by detectives investigating cases of people murdered and secretly buried by the IRA.
At the heart of the case is the 1972 IRA murder of Jean McConville.
US prosecutors have demanded anything in the Boston College archive relating to the death of the Belfast mother of 10, one of the so-called "disappeared".
On Monday, appeal court judges will hear a challenge to this demand.
The case has implications in terms of new legal hurdles and costs for universities that gather historical records of conflicts around the world.
Police in Northern Ireland are seeking accounts from former IRA members who accused Sinn Fein leader Gerry Adams of running a secret cell within the IRA that carried out the kidnappings and disappearance - something Gerry Adams has denied doing or having any knowledge of.
Dolours Price was one of 26 former IRA members to give a series of interviews - between 2001 and 2006 - as part of the research study, called the Belfast Project.
In December, Boston College was ordered by a federal judge to turn over recordings, transcripts and other items related to Ms Price to federal prosecutors acting on behalf of British authorities.
This is the first time they have tried to use the Boston College oral history collection to build criminal cases.
Boston College has already turned over tapes of interviews given by Brendan Hughes, a former IRA member who died in 2008.