Detectives are hunting a "disgusting" man who wipes "sticky liquid" on unsuspecting girls.
Officers are investigating five incidents in which the victims, all young teenagers, discovered the man had put something on them.
The first assault happened at 3.20pm on 13 November as a 14-year-old girl walked along Kennedy Drive in Bury, Greater Manchester.
A man followed her down an alleyway, asked her for the time and stood "uncomfortably" close to her.
When she arrived home she noticed a sticky liquid on the back of her tights, Greater Manchester Police said.
Between 8.05am and 8.20am on 7 December, a 15-year-old girl was walking with her sister and was approached from behind by a man on Ostrich Lane, Prestwich.
She felt a liquid on the back of her tights and the man walked between the two sisters and away.
About the same time that day, another 15-year-old girl walked past a man who turned around and followed her on to St Mary's Road.
Ten days later a 14-year-old girl was in a shop on Mill Gate, Bury, with her mother when a man bumped into her and wiped a white substance on her bottom.
The next day, 18 December, a man followed two 13-year-old girls on Bury Old Road, Besses, near the M60 in Prestwich.
In each incident, the offender was described as being a white man, aged between 25 and 35 who was carrying a bag. On a couple of occasions, he was wearing a fur "trapper" style hat with earflaps.
Detective Inspector Lynne Vernon, from Bury CID, said: "We have five separate incidents and do not know the motivation behind them. While we do not want people to be frightened unnecessarily, we are taking these reports seriously.
"None of the victims were physically harmed in any way but this is still a disgusting act and the person responsible must be caught."
Anyone with information is asked to call Bury CID on 0161 856 8152 or the independent charity Crimestoppers, anonymously, on 0800 555111.