An appeal by members of the group known as the Hooded Men will be heard by the Supreme court in London.
The 14 Catholic men say they were subjected to state-sanctioned torture when they were interned in 1971.
None of the men were ever convicted of any wrongdoing.
The Court of Appeal in the Belfast has previously ruled that an investigation into the men's case should be carried out by police without delay.
However, the PSNI later appealed this decision to the Supreme Court.
In response the Hooded Men have now lodged a cross- appealed this decision.
Hooded man Francis McGuigan said: “It is now 49 years later and nobody has held accountable for the torture that was inflicted on me. It is infuriating that the Chief Constable continues to challenge what two successive Courts have ruled."
Darragh Mackin, of Phoenix Law, said “it is difficult to envisage a case in which touches upon more important issues of law and wider public importance. In taking this case to the Supreme Court in London, we now look forward to the Court taking this opportunity to clarify the law in the field of legacy litigation so that those victims who have also waited too long can now seek justice via the courts."
