The two men were dressed in police uniform and driving a car fitted with blue flashing lights when they stopped a black Audi A1 in East Kilbride.
They convinced the 28-year-old driver to get out and then one suspect drove off in the Audi while the other followed in the grey Volkswagen Passat kitted out as a bogus police car.
The victim alerted police after the incident on Mavor Avenue at around 7pm on Sunday.
Officers said a similar incident occurred around half-an-hour earlier near the First Glass pub on Hamilton Road, Cambuslang.
However, on that occasion the driver refused to leave his vehicle and asked to see the officer’s warrant card. The suspects then fled.
The suspect who approached both vehicles is white, about 5ft 8in and of medium build with short, brown, gelled hair.
He was wearing cargo trousers, a utility belt and body armour - all black - and was seen speaking into a handheld radio.
Detective Sergeant Graeme Begley said: “This causes great concern that there are individuals out there posing as police officers and managing to con members of the public as they go about their daily business.
“I would like to speak to anyone who was in the vicinity at the time either of these incidents took place and who may have witnessed either incident, or perhaps saw the suspects hanging around the areas in their car.
“I’d also like to remind anyone who has any concerns regarding the authenticity of a police officer to simply ask for identification - any legitimate police officer will always be in possession of this and happy to produce when asked.”
Anyone with information about either incident is asked to contact police on 101.