Police are keen to speak to two women who went to the aid of girls who believe they were followed by men in white vans.
Both incidents are said to have happened in Kirton Lindsey earlier this month.
The first was at around 9am on Thursday, September 17, as an 11-year-old walked along Grayingham Road, towards the school.
A man in a small white van is said to have stopped. The driver then left the vehicle and ran towards her.
The girl ran off and a woman in a Land Rover Discovery-style vehicle came to her aid, before explaining what had happened to the girl’s mum.
The woman then drove away.
The man was described as white, aged 40-50, fat, with dark brown hair, and about 5ft 6” tall.
The second incident is said to have happened at around 8.30am on Wednesday, September 23.
Another 11-year-old girl – who is a pupil at the same school - was walking along North Cliff Road, when she became suspicious of a noisy, white Transit-type van with rusting wheel arches, driving slowly behind her.
She went into the Spar shop but when she left a short time later, the van was still there and she became distressed.
A woman – believed to be in her 30s - in a black four-door vehicle stopped, picked her up and took her to school.
The driver of the van was said to be a white man.
Dc Paul Bexon, who is leading the investigation, said: “While these incidents are naturally concerning, it is not clear what happened.
“We would like to trace the women who are said to have stopped and assisted the girls in relation to the incident, in order to ascertain what happened.
“We would also encourage parents to speak to their children about stranger danger.”
Anyone with information is asked to call 101, quoting crime reference number 2139402 of September 17, or log 83 of September 23.
Alternatively, call Crimestoppers on 0800 555111.