They're trying to force the Irish government to apply for the European Court of Human Rights to revisit its decision from 1978 which found that while the 14 men were subjected to inhuman and degrading treatment, they were not tortured.
In the 1970s the so called 'hooded men' were interned and subjected to interrogation techniques including white noise, sensory deprivation and hooding.
The European Court of Human Rights found the techniques used by the British authorities were inhuman and degrading but they were not intense and cruel enough to be classed as torture.
The survivors claim new evidence has come to light that shows the British government withheld vital evidence and they now want the Strasbourg court to review its decision.
However it's up to the Irish government to apply for the case to be reopened. The deadline is next Thursday and so far there's been no indication of what steps, if any, will be taken.
A High Court action brought by the survivors to try and force a government decision will be heard today.
They claim the government's inaction is interfering with their fundamental rights.
