Senior judges in Belfast have set aside a full day for the appeal being mounted by the Sinn Fein leader.
Mr Adams is challenging convictions in 1975 for two alleged attempts to escape from detention.
He was among hundreds held without trial under an internment programme introduced by the British government during the early years of the conflict in Northern Ireland.
First interned in March 1972, he was released in June that year to take part in secret talks in London.
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Mr Adams was rearrested in July 1973 at a house in Belfast, and interned again at the Long Kesh camp.
On Christmas Eve 1973 he was one of three prisoners apprehended by wardens while allegedly trying to cut their way through its perimeter fencing.
In July 1974, according to government files, he again attempted to escape by switching with a visitor.
He was later sentenced to 18 months in jail for attempting to escape.
The Louth TD’s bid to overturn his convictions centres on the recovery of a document from the National Archives in London.
During a review at the Court of Appeal in Belfast Lord Chief Justice Sir Declan Morgan confirmed a January date for the hearing.
An issue was also raised about the state of some old microfiche documents which feature in the case.
Sir Declan said it was difficult to read parts of the material and urged the parties to provide any written assistance.