On Friday, detectives investigating the incidents on board Thameslink trains between Sussex, Kent and Bedford released CCTV images of a man they would like to speak with.
The three incidents happened during the summer, police said. The first was on a train between Blackfriars and Horley Times station, the second on a train between East Croydon and Bedford, and the third incident happened on a Bromley South to Otford Time train.
In each incident, a man was seen to expose and touch himself inappropriately in front of passengers, police said, but officers now believe these incidents are linked.
The police suspects that the man shown in this CCTV image may have information which could help them investigate.
If you know who he is, contact BTP by sending a text to 61016 or by calling 0800 40 50 40 quoting reference 74 of 11/08/2018. Or you can call Crimestoppers anonymously on 0800 555 111.