The first incident started outside Bambinos takeaway on Kings Road when one of the group attacked a 26-year-old man.
The victim, who was punched to the head, fell backwards into the road.
A few minutes later the same group were involved in an altercation outside Harrogate International Centre.
It resulted in one of the group punching another man to the head.
The incidents took place within five minutes at about 4.30am on May 28, but details were only released today as police appealed for witnesses.
A North Yorkshire Police spokesman said: "If members of the public were present and can offer any information or evidence which would lead to the identification of the suspects this would be beneficial to the case.
"The first victim was dressed in light coloured shorts and a light coloured t-shirt at the time.
"We are conducting enquiries and are requesting the public’s assistance to help determine the full circumstances surrounding the incident.
"In particular, we are appealing for information about the identities of the suspects involved."
Anyone with information is asked to call 101, select option 2, and ask for PC 437 Akram, or pass information on to Crimestoppers in confidence on 0800 555 111.
Quote the North Yorkshire Police reference number 12170093568.