They are warning motorists are using a back street at Granville Crescent, Stainforth, as a shortcut to avoid speed bumps on the main roads nearby.
One resident told how her husband's car was written off after a pick-up truck crashed into it while it was parked.
South Yorkshire Police and Doncaster Council have both been told of the concerns. Speeding across Stainforth in general is a issue that has already been raised by Stainforth Town Council.
The resident, who asked not to be named, said: "I have been in contact with both the police and the council about the speeding vehicles but have had no success in getting the matter resolved.
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"The police say they cannot place speed cameras down the backs as it is not safe to do so, and the council have said they cannot justify putting sleeping policeman down the backs as there have not been enough incidents reported.
"I myself have had damage to my car on numerous occasions and these have been reported to the police and on September 24 my husband had just parked his car when a speeding pick-up smashed into the side of the car causing the car to be dragged down the backs.
"The pickup then had to reverse to unattach the car and drive off without stopping, causing utter devastation to the car.
"There are speeding vehicles constantly using the backings to dodge the speed bumps on Emerson Avenue and Princess Avenue.
"Children play down these backings and it is going to take someone to be killed before anything is done. I have lost total faith in the police and the council are not interested."
Gill Gillies, assistant director for environment at Doncaster Council, said: “We are very concerned to hear of incidences of anti-social driving and speeding at this location. The area is in a 20mph zone, but of course safety does rely on drivers being responsible, driving appropriately to the conditions and within the law.
“In order to give the greatest benefits to communities across Doncaster, improvements such as traffic calming are prioritised to the areas with the worst problems. This situation is regularly reviewed, and particular attention will be given to this area in considering priorities for the future.
“In the meantime, we would be supportive of any enforcement action undertaken by South Yorkshire Police.”
Police Sgt Mark Gregory said: “We are aware local residents have raised concerns about speeding concerns in the Stainforth area. I would like to offer my reassurance that we closely monitor reports of speeding and carry out specialist operations to target anyone putting others in danger, by going over the speed limit.
“We also work closely with the Camera Safety Partnership who along with PCSOs, have been conducting high visibility patrols in the area to address speeding, engage with the local community and provide reassurance.
“This activity will now continue and I would encourage anyone with concerns around speeding issues to report it via 101, or speak to a local officer in the area.”