Detectives in North Yorkshire said they had received two reports of indecent exposure to young girls, which may involve the same man.
In the latest incident, the driver of a black VW Polo stopped on Mowbray Road in Catterick at about 12:30pm and indecently exposed himself to a young girl. He was described as having black or dark brown hair and was wearing square shaped glasses.
In the earlier incident, a man matching a similar description pulled up in a black VW Polo or similar-looking car on Benkhill Drive in Bedale and performed a "lewd act" in front in a 10-year-old girl. It happened at about 3:30pm on Saturday.
Neither girl was injured but both are said to be upset.
More top news
Newcastle City Council leader tells ITV News Tyne Tees that the city can settle "several dozen" child refugees from Calais' migrant camp.
ITV News Tyne Tees has learned that 3 councils in the North East will do their own devolution deal with Westminster.
The Environment Secretary says she expects improved flood defences at the Foss Barrier in York to hold up in future.