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
Emma brings you Monday night's forecast
Campaigners have been taking part in a protest walk today in opposition to a planned building development in Newcastle.
The farming and rugby communities in Tynedale have rallied to help a Northumberland man diagnosed with an inoperable brain tumour.