British Transport Police have also arrested a man in connection with a separate allegation of racial abuse on the railways.
A group of 10-12 boys aged between 14 and 17 shouted racially offensive remarks and threw objects at a 44-year-old waiting at Motherwell station on Wednesday, before one of the group spat on a 25-year-old woman.
The group boarded the 6.20pm Glasgow to Lanark service at Bellshill, where they are reported to have acted in a rowdy and disorderly manner.
They got off at Motherwell shortly after 6.45pm and attacked the man and woman, and a fire extinguisher was also stolen and discharged around the station.
Detective Constable David Merchant, the BTP officer in charge of the inquiry, said: “This sort of appalling behaviour is unacceptable and I am appealing for anyone who was on the train or at the station and can provide information which can help identify the youths responsible.”
Meanwhile, BTP have arrested a 25-year-old man following an unconnected allegation of assault on a 20-year-old woman and alleged racial and abusive behaviour on a train travelling between Aberdeen and Perth on July 15.
A report will be submitted to the procurator fiscal and inquiries are ongoing to trace a second man in connection with the incident.
BTP also revealed that an arrest has been made in connection with a third unconnected incident at Dalmeny, near Edinburgh.
A 37-year-old man has been arrested after a 53-year-old woman was allegedly assaulted on board a train travelling between Edinburgh and Perth on October 3.
A report has been submitted to the procurator fiscal in connection with the incident and he will appear at Edinburgh Sheriff Court.