Last Friday a man in a white van reportedly exposed himself to at least one woman in Grange Road in Saltford.
And this week a student walking home from school was left distressed after she was approached by a man in the same road who tried to entice her into a white van.
Wellsway School in Keynsham has reminded to walk home in groups and not to speak to any strangers.
A spokesman for Avon & Somerset police said today: “At this stage, we are keeping an open mind as to whether these incidents are linked or not.
“We have increased patrols in the local area and would ask anyone with further information to contact us on 101.
“Any further incidents should be reported to us immediately.”