Uniformed officers arrested the trio, aged 19, 21 and 27, in the city centre on Sunday afternoon.
When they searched the car, items were discovered which led to them being arrested under the Terrorism Act 2000.
Police are not revealing exactly what was found but have confirmed the items were not explosives.
The men were still being quizzed by officers last night.
The car the suspects were using turned out not to be stolen.
The three UK residents appeared before a District Judge in Manchester yesterday afternoon. An application was granted for the suspects to be held for a further 72 hours.
The M.E.N. was in court when their names were read out but was required under the terms of the act to leave the court while the proceedings were held in secret.
The application to extend their time in custody, lasting just under an hour, was made by Crown lawyers on behalf of Greater Manchester Police. A senior officer from GMP was in court.
A statement from Greater Manchester Police said: "At around 1400hrs on Sunday 13 March, uniformed officers on routine patrol in Manchester city centre spoke to three men aged 19, 21 and 27 regarding a car they were using. It was believed that the vehicle was stolen and therefore the men were arrested on suspicion of taking a motor vehicle.
"The vehicle was then searched and several articles were found in the car which raised concerns with the officers. The three men were then arrested under the Terrorism Act.
The investigation is ongoing but GMP can confirm that no explosive devices were found in connection with this incident.
"The officers' actions were part of an overall strategy of vigilance in relation to the possibility of terrorism and were part of GMP's commitment to keeping Greater Manchester safe."
secret courts... under the terrorism act....
is anyone else screaming this around their town?