A 12-year-old girl with a cast on her arm and two elderly women were targeted in a spate of handbag thefts.
The first bag was stolen at about 10am on June 21 from an 89-year-old woman in the town centre near Grove Road, Eastbourne.
The thief was wearing multi-coloured shorts and grabbed her maroon leather bag as he rode past her on his bike.
Between 8pm and 8.30pm that day a 12-year-old girl with a plaster cast on her right arm was targeted as she got off a bus near Waitrose in Old Town and went into Gildredge Park.
A teenager followed her into the park and tried to grab her white satchel but the bag caught on the plaster cast and the thief ran away.
The thief was 16 to 18 and tanned with short hair. He had a deep voice and was wearing a black NY cap, a plain black hooded top with white zips, grey trousers with darker coloured pockets and white high-top trainers.
The third incident happened at about 10.30am on Sunday 22 June when a thief grabbed a red leather handbag from an 87-year-old woman in Mountney Road, Eastbourne.
The victim was walking towards the church and the junction with Charleston Road when a young man on a bike grabbed the bag from her and rode off towards Green Street.
The thief was wearing a red jumper or hooded top and dark coloured shorts.
Police officers do not know if the same person is responsible for all three crimes but are considering the possibility the offences are linked.
Detective Constable Sean Stapley said: "The description of the offender in each case suggests that one person is responsible for all of them but we cannot be sure at this stage.
"I need to speak to anyone who was in the area close to where any of the crimes happened who may have seen the thief escaping.
"It is also possible that there are victims who have not come forward because they are upset or embarrassed by what happened to them. Please come forward. You may have information that could be vital to us without you even knowing it."
Anyone with information should call 101 quoting serial 532 of 21/6, email firstname.lastname@example.org or call the independent charity Crimestoppers anonymously on 0800 555111.