One of the men being questioned about the murders of two British soldiers in Antrim on 7 March is refusing food in protest over his detention.
41-year-old Colin Duffy, a former IRA member, was arrested by the PSNI on 14 March.
In a statment tonight, Mr Duffy's family members said the PSNI's motives were based on vindictiveness and were a reaction to media freenzy.
The statement said Mr Duffy has been refusing to take food since his arrest.
The authorities have the option to seek approval for up to 28 days detention when dealing with terrorism investigations.
Detectives investigating the murders have been given more time to question three suspects who were arrested last weekend.
The PSNI say they were granted permission to question a 41-year-old man and a 31-year-old man for a further seven days.
The police have also been allowed a further six days to question a 21-year-old man.
Meanwhile, it is understood that a man who is being questioned about the murder of PSNI officer Stephen Carroll is refusing food.
The 31-year-old man was arrested in Craigavon on 17 March.
