Two schoolgirls were approached by hoodie-wearing men on their walk home from Melksham Oak School last Wednesday.
They were near The Pilot pub when two white men, in their early 20s, appeared.
The following day, two 12-year-olds were approached by two men and a woman in a small silver-blue car, trying to sell cigarettes and alcohol, near the town's Manor School.
Police have stepped up patrols.
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