Patrols are being stepped up in Crawley after a number of reports of women being approached by men over the last week.
Police said they do not believe all of the incidents are linked.
The first report involved a woman jogging in Grattons Park at around 10am on Thursday (May, 21).
She was heading along the pathway towards Peterhouse Parade when a man appeared from the bushes and made an attempt to grab her around the waist.
The victim managed to evade the suspect, described as white, around 50 years old, with grey hair and a flushed face.
At around 7pm on Monday (May, 25), a second woman was jogging along Haslett Avenue when she was approached by a man who put both arms around her waist.
The woman broke free and ran to safety.
This suspect is described as black, around 5' 8", and wearing a winter coat and black rucksack.
Two further reports were made to police on Tuesday (May, 27) of women being approached by a man at Woodfield Road Playing Field.
The first happened at around 6pm and the other at around 6.30pm.
In both cases, the women reported being harassed by a man who was asking a lot of unusual questions and standing too close, but no physical contact was made.
The man was described as Asian, in his 30s, around 6' tall, of slim build and with a black beard.
He was reported to be wearing a hat, possibly a sports cap, and casual clothing, including colourful, modern trainers.
CI Shane Baker said:
"We understand these incidents are very worrying for those involved, and for those who live in the area.
"At this time, we are treating these as isolated incidents.
"We are investigating each case and following all reasonable lines of enquiry to find those responsible.
"Our officers are conducting high-visibility patrols in the town and we continue to encourage people to report any suspicious behaviour to us so we can act accordingly."
Anyone with information is asked to contact 101.
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