It occurred at 4.10pm on Wednesday 23 May 2012, on the Carperby to Askrigg road, and involved a green Volkswagen Polo and a silver Skoda Octavia.
At the time of the incident the Polo was travelling from Carperby towards Askrigg, when it left the road before hitting a tree and then colliding with the Skoda, which was travelling in the opposite direction.
The driver and front seat passenger, who are both 83 and from Askrigg, were taken to James Cook University Hospital where they remain in stable conditions.
The 59-year-old man, from the Northallerton area, who was driving the Skoda was not injured in the collision.
The road was closed for just under five hours.
Traffic Constable Martin Mulcaster, of North Yorkshire Police’s Roads Policing Group, said:
I would like to speak to anyone who may have witnessed the collision or may have seen either of the vehicles prior to the incident. I ask them to contact the police as soon as possible.
If you can assist with this enquiry please contact North Yorkshire Police on 101, press 2 and ask for Martin Mulcaster.