The youths, who are aged 16 and 17, were walking to the Cityside via Ebrington Square with a group of friends after the fireworks display soon after midnight on Saturday.
Two males in prison costumes walked past nudging one of the youths and taking a baseball bat that was part of the others fancy dress costume.
The two teenagers walked across Limavady Road.
The two assailants then crossed the road and assaulted them.
One of the teenagers was taken to hospital by ambulance with injuries to his face, back and hands. The assailants ran off towards Foyle Fold.
Police are keen to hear from anyone who can help identify them.