Police have increased patrols after the incidents on Wednesday (March 6) and today (Friday, March 6).
On Wednesday at around 8.20am a nine-year-old girl and a 12-year-old girl were walking in High Street, Tarring, on their way to school when a man approached them from behind.
The younger girl felt a hand on her shoulder and when she turned and saw the man, both girls ran to their school.
The suspect, who covered his face when the victim looked at him, was white, thin and wearing black shoes, a black hooded top with the hood up and black trousers.
A 12-year-old girl was approached by a man at about 8.40am this morning in an alleyway between High Street and Bellview Road.
A man described as being in his late 60s or early 70s blocked the path of the child and tried to speak to her.
A woman walking nearby intervened, led the girl out of the alley and made sure she was ok.
The man had grey thinning hair and was wearing a red knee-length coat and beige trousers. He had two front bottom teeth.
Sergeant Mandy Symes said: “There is nothing to suggest that the children were in any harm but we have to investigate just in case. We want to speak to both men to find out what their motive was for speaking to the girls.
“We need to speak to anyone who was in High Street or the alleyway between the road and Bellview Road around the time of the incidents, or who uses either of them and recognises the description of either man.
“We have increased patrols in the area as a precaution and will be talking to all the schools in the area to ask that children are reminded not to speak to strangers.
“If you know anything at all about what happened, please contact us.”
Anyone with information should email [email protected] quoting serial 493 of 04/03, call 101 or contact the independent charity Crimestoppers anonymously on 0800 555111.