Police have three separate reports of a man approaching women and exposing himself to them as they walk along Empingham Road in Stamford.
Officers are appealing for anyone that may have been approached by this man, who has then exposed himself, and has not yet reported this to police to come forward.
Police would also like to hear from anyone who thinks they have seen a man acting suspiciously in the area but may not have gone on to commit any offences.
The first offence happened about 7.30 pm on Tuesday March 13, the second at about 8.45pm Monday March 19 and the third offence reported to police happened about 10.40pm on Thursday, April 5.
A police spokesman added: "We think there may be other people who have been approached and have not thought to give us a call. We are determined to locate this man and stop this criminal and offensive behaviour."
Sgt Emma Crisp, Neighbourhood Policing, for Stamford, added "We are and will continue to patrol Empingham Road and the streets around. Please speak to one of our officers or call on 101 if you have concerns or are worried by anyone's behaviour.
"We have not provided a description on this occasion as we would like any witnesses to tell us what they have seen and provide their own accounts."
If you do know anything about these incidents, please contact police by emailing [email protected] with incident number 519/04 in the subject box.
Alternatively call 101, quoting incident number 519 of 4 April.