The incident occurred on board the 8.15am Virgin Trains service from Manchester Piccadilly to London Euston on Thursday, 5 March.
Investigating officer, PC Emma Power said: “A man boarded the train at Piccadilly and sat next to the 19-year-old. He immediately began touching her leg and thigh. She asked him to move so she could get out of the seat and eventually he moved aside so she could make her way to the vestibule.
“The man followed her into the vestibule and continued his sexual assault until two other passengers entered the area.
“The man got off the train when it arrived at Stockport but the victim waited to disembark until she saw him walk towards the station exit.
“As she made her way from Stockport railway station to the bus station the same man grabbed her arm and despite attempting to pull away the man maintained his grip until she eventually managed to escape.”
The man in the pictures travelled to Manchester Piccadilly via a Manchester Airport train which he boarded at Burnage. Officers are urging him or anyone who recognises him to come forward to help assist the investigation.
PC Power adds: “This was an absolutely terrifying experience for the victim and she remains shaken and upset by what happened. It is vital we track down the man who did this. Everyone has the right to travel in safety and without fear of shocking behaviour like this.
“We urge the man in the CCTV stills or anyone who thinks they might recognise him to contact police.”
Anyone with information is asked to contact British Transport Police on 0800 40 50 40, or text 61016, quoting reference PSUB/B9of 27/03/2015. Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.