The two wounded men, aged 57 and 58, were assaulted as they walked along Castle Street near to the Lidl car park at around 1.20am on Sunday, September 12.
The men were assisted by members of the public and were treated for facial injuries at Royal Alexandra Hospital in Paisley.
Their current condition has not yet been confirmed.
The first suspect is described as a male in his 50s with wavy grey hair. He was wearing a green jacket with orange lining in the hood.
The second suspect is described as a male aged around 18 years old with red hair. He was wearing a bright orange t-shirt and blue jacket.
Officers are appealing for information following the attack.
Those who were in the area at the time of the assault last Sunday and may have seen anything are being urged to get in contact with the police.
Detective Constable Imran Abuzar, of Clydebank CID, said: “This was an unprovoked attack in which two men required hospital treatment for their injuries.
“We are appealing to anyone who may have been in the area around the time of the assault and may have seen what happened to get in touch.
“Anyone with information is asked to contact Police Scotland on 101, quoting incident number 0353 of 12 September, or make a call anonymously to the charity Crimestoppers on 0800 555 111.”