A man and a woman continue to be questioned under the Terrorism Act after being arrested at Holyhead port.
Police said there was no threat to any port passengers
North Wales Police said the man, 47, and woman, 44 - originally from Algeria - were arrested last Friday.
On Thursday, a district judge granted detectives a further five days to continue to question the pair. Officers are liaising with other police forces.
A force spokesman emphasised no threat was posed to passengers and staff at the port as a result of the arrests.
Deputy Chief Constable of North Wales Police, Clive Wolfendale, has said the arrests were not directly linked to last week's alleged foiled bomb plot to blow up planes, but said officers were keeping "an open mind".
He said the arrests were intelligence-led and carried out by Special Branch officers.
'Result of intelligence'
The couple who were arrested were originally from Algeria, but police have not confirmed whether they were now British citizens.
Mr Wolfendale said: "As far as we know they were not travelling together.
"Our understanding is one of the individuals travelled across from the Irish Republic using a ferry and the other arrived independently from elsewhere, probably England.
"The arrests were as a result of intelligence. We are working very closely in conjunction with colleagues in other forces, in particular the Metropolitan Police."
Police said they were arrested because they were in possession of "several items" but have not disclosed what the items were.
Police also did not reveal whether the pair were related or married.
They are being held at separate police stations in north Wales but inquiries are being made outside the force area. Security had been stepped up at the port following last week's terror alert.
Holyhead is a main ferry terminal for services between north Wales and Ireland.