Two women were targeted in separate assaults in Mangotsfield on Sunday (July 21).
In the first incident, a woman was running along the cycle path between Old Station and Rodway Hill at about 8.15am and passed a man, police say.
Shortly afterwards he ran up behind her and grabbed her waist. She flagged down cyclists on the cycle path and the man ran off.
The second incident happened at about 8.30am on the cycle path near Pomphrey Hill when a woman who was walking her dog was asked for directions by a man.
About 10 minutes later he pushed her from behind and ran off.
An Avon and Somerset Police spokesman said: "The two incidents are being linked and police investigations are continuing.
"Police patrols are providing reassurance in the area and also taking information from members of the public.
"Anyone with information is asked to contact us quoting references 5219166474 or 5219166466."
Safety advice aimed at joggers and dog walkers who use cycle paths and other walkways is available here.
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