Police described the approaches as "utterly shocking" and said officers would be patrolling the Kilcooley area of the town to reassure residents.
Children were approached in Rostrevor Drive on Sunday, and in Kircubbin Gardens and Glastry Court on Monday
None of the children were physically assaulted during any of the incidents.
In the first incident at about 17:00 GMT on Sunday, two nine-year-old girls were approached by a man in Rostrevor Drive who walked into an alleyway before unfastening his belt.  Both girls ran away.
At about 16:00 GMT the following day, an eight-year-old girl told police she was approached by a man  in Kircubbin Gardens.
About an hour later, a man exposed himself to a seven-year-old girl in Glastry Court.
The suspect is described as being in his 30s, about 5ft 7in tall and was wearing a blue top.
A man exposed himself to a seven-year-old girl in one of three "suspicious approaches" to children in Bangor, County Down, over a two-day period.