Falmouth police are investigating reports of a man approaching and following women, causing them distress.
Officers say they have received a number of complaints that a man in his late 40s or early 50s driving a clean, fairly new white van with no markers, has been following women who have been running.
Pc Andy Hocking said: "He has also been heard to make suggestive comments that have unnerved and upset the women.
"We have had unconfirmed reports that the male may have also exposed himself."
The reports have occurred between 7am and 9am around the town centre and the Pendennis Headland area.
"We are taking this very seriously and would urge anyone who have experienced similar problems to get in touch," added PC Hocking.
A possible suspect has been identified, but no arrests have been made.
Anyone with information can call Falmouth station on 101 or through Crimestoppers on 0800 555 111.
