A man in his 20s was taken to hospital after paramedics were alerted to an assault at a house in the Creggan Road area, at about 1am on Sunday.
At about 5am, the Fire and Rescue Service were called out to a fire at the property and a second man had to be taken to hospital.
Neither man is believed to have sustained life-threatening injuries.
"Police believe the fire was started deliberately by two other men who were in the area and are appealing for information about them," a PSNI spokesperson said.
A motive for the incidents has not yet been established.