The first man was attacked at 10pm on Wednesday when he cycled on the pavement past a group of three other men in Devonshire Avenue, Southsea.
One of the group chased him. But when the victim stopped the bike he was punched to the ground.
The attacker continued to punch and kick him until he lost consciousness.
One of the trio was white, between 18 and 25, 5ft 9ins tall and was wearing a grey tracksuit, black trainers and had a black bag.
Police are linking the incident to one in Bradford Road today in the early hours just after 12am.
The victim was also on a bike and was in a cycle path when a man walked out in front of him.
The cyclist rode around him but a second man started being aggressive.
Police said the victim was then punched to the head and ribs several times.
Call police on 101 quoting 44170127667.