Vehicle has experienced, unexpected, slight and brief, acceleration 3 times at highway speeds up to 60 mph. The 4th incident was an uncontrolled acceleration when parking behind another parked vehicle. Car accelerated into the backend of parked vehicle. Operator was at a complete stop and needed to pull forward a few feet. They took foot off of brake and lightly pressed the gas peddle. The car unexpectedly surged forward hitting parked car. 1 day later we received an email from Hyundai Blue Link stating that "a possible condition with your Engine Control System has been detected" and recommends bringing in for service for a full system check. Both cars were damaged and Tuscon had to be towed to a repair shop.