Bangor Police and Bangor school officials said two William S. Cohen school students reported having been followed by a middle-aged man driving a gray SUV.
The incident happened last Friday on Garland Street.
The man allegedly exposed himself to the students before driving off.
Police have been looking for days but have not been able to identify a suspect. They are continuing to patrol Bangor schools regularly and work with school officials.
Superintendent Betsy Webb said safety is the Bangor School Department's No. 1 concern.
"The principal talked with all students and felt it was a good time to review the safety protocols, making sure students know not to talk to strangers, to have a safe route home and to follow that route," said Webb.
On Monday, a student reported a parent offered for them to wait in their car at the bus stop. The student did not know the parent.
A similar incident happened on Wednesday when a student was offered a ride to school.
Both were Cohen School students and both incidents were reported.
School officials believe both of these incidents were well-intentioned but said the students did the right thing by reporting it.
William Cohen School Principal Michael Missbrenner sent a letter home to parents, reminding them of how to keep their kids safe.