A 13-year-old girl ran away when a stranger told her to get into his black van, in Oswestry.
Six days earlier an 11-year-old boy, in Weston Rhyn, ran off when a man in a black vehicle claimed he had been sent by his mother to fetch him.
Now West Mercia Police have published a sketch of the person they want to talk to about these incidents.
Anyone who thinks they recognise the man in the picture is urged to contact them immediately.
The 13-year-old girl was approached at 7.50pm, on Tuesday, October 18.
She was walking along Longueville Drive, Oswestry, towards its junction with Aston Way.
The driver of a small black van pulled up to her and told her to get in.
She would not and ran off instead. The man, who was of medium build, white and in his 20s, stayed in his vehicle, which had a blacked out rear window.
It is said he had a Liverpudlian accent. No one else is thought to have been in the van.
The vehicle would have seemed odd to passers-by because the registration plates were covered by bags, or black tape.
The 11-year-old boy was approached in Weston Rhyn, on Wednesday, October 12, at around 3.55pm.
He had just got off the school bus when a man shouted to him claiming he had been sent by his mother to fetch him.
Again the man was said to be white and have a Liverpudlian accent. His car is believed to have been a black Renault Clio.
He was said to be in his late 20s, have short, straight brown hair and be thinly built.
When the boy ran away the stranger drove off towards Trehowell Lane.
Detective Inspector Mark Jones, said he was keen to hear from people who recognised the driver from the sketch, or by his description.
Anyone with information should ring, ‘101’, ask for West Mercia Police and quote incident number 481s, of October 12, or 308s, of October 18.
Information can also be given anonymously via Crimestoppers, on 0800 555 111, or through their anonymous online form (click here).
No personal details are taken. Information cannot be traced, or recorded.
People giving information anonymously do not go to court.