British Transport Police have released an image of a man following reports of indecency offences on board trains travelling between Perth and Inverkeithing, and at Inverkeithing Railway Station.
The incidents happened between Monday June 5 and Wednesday June 7.
Anyone who knows the man in the photograph is asked to get in touch with the BTP as soon as possible.
The man is described as being aged between 50 and 60 years, and about 5ft 8in in height with short grey hair. He was wearing glasses and an oversized black two piece suit, black jacket, white shirt and black shoes.
Investigating officer Detective Constable Nick Ritchie said: “These were very distressing incidents for the victims of each incident and I am looking to speak with anyone who knows the man in the image we have released.
“Behaviour such as this will never be tolerated and we are actively pursuing a number of enquiries.”
Anyone with information can contact transport police by sending a text to 61016 or by calling 0800 40 50 40 quoting reference 1700040146. Information can also be given anonymously to Crimestoppers on 0800 555 111.