Celtic fans have been accused of singing sectarian songs on a train following their side's 3-3 draw with Inter Milan at Parkhead in the Europa League on 19 February.
British Transport Police (BTP) said the singing is believed to have happened as the 11.36pm service travelled between Gleneagles and Perth shortly after midnight.
The men are thought to have been on their way home from Celtic Park, where the Hoops scored a last-minute equaliser to earn a draw against Italian giants Inter Milan in a fixture that was a repeat of the 1967 European Cup final.
Constable John McErlane, the BTP officer in charge of the inquiry, stated this behaviour will not be tolerated by BTP and is appealing for anyone who was on the train and has information to come forward.
He said: "It is believed the men were returning from a Europa League match in Glasgow. There really is no need for such unsavoury behaviour on the rail network and the actions of the men disgusted other passengers, prompting complaints and I am anxious to speak with anyone who witnessed it to get in touch."
BTP can be contacted on 0800 40 50 40 or by texting 61016 – quoting reference B5 of 02/03/2015.
Information can also be given anonymously to the independent charity Crimestoppers.