Kent Police are investigating a number of reports in recent weeks of people travelling around in vans and approaching children.
Officers said some people have been wearing clown or Halloween masks in a bid to try to scare pupils walking to and from schools.
Parents and children in Tunbridge Wells and Tonbridge have now been urged by police to be vigilant following the “suspicious incidents”.
Chief Inspector Dave Pate, of Kent Police, said: “We are still working to establish whether any offences have been committed.
“However, I want to assure parents that we take the safety of all children very seriously and have extra officers on patrol around schools.”