The PSNI say officers arrested the men aged 22 and 26 in the London Street area this morning after the silver Renault Megane car they were travelling in failed to stop for police.
The car was chased by pursuit trained officers.
The pursuit ended when a police vehicle was struck by the Megane in London Street, injuring three PSNI officers.
A number of vehicles were damaged in London Road, Upper Frank Street and My Lady’s Road as a result of this incident.
Two members of the public have also reported injuries.
None of the injuries are believed to be serious at this time.
Inspector Wise said: “The two men are currently in custody assisting officers with their enquiries and I would ask anyone who witnessed the silver Renault Megane being driven in the area this morning or who witnessed the incident to contact police in Musgrave police station on 101.”