Independent republican candidate Gerry McGeough has been arrested over "serious terrorist crime".
Gerry McGeough is being questioned about terrorist offences
Mr McGeough, 46, a candidate in Fermanagh and South Tyrone, was arrested after leaving the count centre in Omagh on Thursday.
It is understood he is being questioned about the attempted murder of a UDR member in 1981.
The husband of a Sinn Fein councillor in Monaghan was arrested in Aughnacloy. Police said both arrests were linked.
The second man arrested was Vincie McAnespie, 44, whose brother Aiden was shot dead by the army in Aughnacloy in 1988.
His wife, Brenda McAnespie, said the arrest of her husband had traumatised her children.
"This is the sort of policing we need to stop," she said.
Police said both men were being questioned about serious terrorist crime dating back several years.
Sinn Fein MP Michelle Gildernew called for Mr McGeough's release, describing the arrest as "political policing".
The party's president Gerry Adams also said Mr McGeough should be set free.
"He was campaigning openly and attended one of our meetings. He should be released," he said.
Brenda McAnespie said the arrest traumatised her children.
However, the police have said they took a number of factors into consideration before making the arrest.
"Police became aware that this individual had re-entered the jurisdiction some time ago but it was not possible to effect an arrest immediately because of the complexity of the investigation and the need to recover and re-examine evidence dating back many years.
"Police acted as soon as the required operational processes had been completed and the appropriate resources were in place.
"The rationale for the arrest and its timing was based on the police obligation to investigate serious crime," a PSNI statement said.
Mr McGeough, who received 814 first preference votes on an anti-PSNI ticket, is being held at Antrim PSNI station.
It is believed he is being questioned about an incident in 1981 in which an off-duty UDR man was shot at while he was in a van.
He was able to return fire with his personal protection weapon and injured one of his IRA attackers.