Officers want to trace the driver of a white coloured Mitsubishi jeep style motor vehicle after the boys aged 14 and 15 are alleged to have been verbally abused and photographed while walking in the Murray Street car park in the town between 9 pm and 9.30 pm on Saturday.
The boys were making their way from Greenlea Road in the town to Ednam Street and were cutting through the car park when the driver of the vehicle passed them, stopped, and on alighting from the vehicle is said to have shouted and sworn at the boys.
He was also seen to take photographs of the boys on a mobile phone.
The driver is described as being male, in his 40s, about 5′ 6″ tall, heavy build, short dark hair and was wearing a black jumper and trousers.
He spoke with a local accent.
PC Jim Tweedie at Annan Police Station said: “We are keen to hear from anyone who may have seen this white jeep style vehicle or the driver on Saturday night or who witnessed this incident.
“We would also ask the driver of the vehicle himself to come forward to explain his actions in this incident.”
Police at Annan can be contacted on 101.