A man verbally abused a group of Asian men aboard a train and gestured to suggest he wanted to slit their throats, British Transport Police said.
Officers are trying to trace the suspect, who boarded the Scotland-bound service at Preston and got off when the train stopped at Lancaster.
The group was racially abused and threatened aboard the train between 10.40am and 11am on July 16.
PC Allan Fernie said: “The three men, who are all Asian, were travelling to Glasgow and were minding their own business when they were targeted by a fellow passenger.
“The man initially engaged the victims in conversation, but then began to racially abuse them and then threatened them – making a gesture as if to slit their throats.
“Investigations to date have revealed the abusive man boarded the train at Preston and left the service at Lancaster.
“Everyone should have the right to travel on the railway without encountering abuse, violence or hatred in any form.
“Thankfully the rail network is relatively crime free, but a minority still seem intent on causing problems for others using trains.
“British Transport Police (BTP) is determined to further drive down crime and I am convinced someone will be able to help with this investigation.”
Anyone who has any information about the incident is urged to contact BTP on 0800 40 50 40 or Crimestoppers, anonymously, on 0800 555 111 quoting log reference B8/NWA of 5/9/13.