South Yorkshire Police say that at about 1pm today (Thursday), a blue Ford Focus was travelling along Southey Green Road, towards Southey Green, when it is thought to have been overtaking a JCB, travelling in the same direction.
During the overtake, the Focus collided with a red VW Golf, travelling in the opposite direction.
Two people in the Focus, a 74-year-old woman and a man, also in his 70s, have been taken to hospital with suspected serious injuries.
The driver and a passenger in the Golf are said to have left the scene before emergency services arrived and police would like to hear from anyone who saw what happened, or know who may have been driving the Golf.
Call 101 quoting incident number 361 of 12 January 2017.