Both arrests were made in the north of the borough after a series of incidents involved cars in and around Bentley, and sheds in Scawsby.
Insp Adrian Luscombe, from the South Yorkshire Police Doncaster West neighbourhood policing team, said: “We recently saw a run of vehicle break-ins in Bentley – but after making an arrest, we are hoping that may now stop.
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“Our officers on patrol found a man hiding in a garden on Sprotbrough Road on February 1. He turned out to be in possession of tools which had been taken from a vehicle earlier.
“On top of that, CCTV was found of him trying to break into a car on Northfield Road.
“Not far away, in Roman Ridge, near Scawsby, we had seen a run of shed break-ins.
“But a man was caught after trying to break into a shed to steal bikes. He was arrested on February 16.”
Police stepped up patrols over car crime this month, after 33 ‘keyless’ vehicle thefts have been reported in the town, with 23 vans among those taken.
Earlier this month, officers revealed that between December 7 and January 10, the force received 101 reports of vehicles being stolen without their keys. Cars with keyless entry systems unlock automatically when the key fob is nearby.
Motorists are being urged to use steering wheel locks to deter thieves.
Keys can also be placed in signal blocking pouches which block any wireless signals such as cloning devices.