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
'Boro finally won a game in 2017 and recorded a first double of the season by hanging on for a 1-0.'
They are renowned as being the finest and most complete medieval city walls in England.
Cancer battler Bradley Lowery was taken to hospital with 'horrendous pain' as doctors fear the disease is progressing.