The probe is based on two incidents that the company reported through the government's "Early Warning Reporting" system, CNN said.
In one of these cases, a universal joint that helps connect the steering wheel and the front wheels allegedly came loose, causing a total loss of steering. In the second case, the universal joint was loosened, but not completely separated, by a defective bolt.
Neither crash caused any injuries and both cars were repaired and returned to the owners.
Hyundai has not yet received a formal request for more information about the cases.
"Of course, we plan to cooperate fully in this investigation," Hyundai spokesman Jim Trainor said.
Both cars were made at a plant in Alabama in the same month. Neither had been driven for more than 600 miles.

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