The pair were injured when a black Volvo V40 and a white Renault Master box van crashed on the B1261 at Irton on Friday afternoon.
It happened at around 1.50pm close to the junction with Irton Moor Lane, North Yorkshire Police said today.
Both drivers were taken to Scarborough District Hospital by ambulance with serious injuries.
A spokesman said one driver remained in hospital in a serious condition.
"We are appealing for witnesses or dash cam footage of the collision or anyone who recalls seeing either of the vehicles prior to the collision, to get in touch as soon as possible to assist the investigation," he said.
"In particular, we are appealing for information regarding the manner of driving of the white Renault box van at the time of the collision or on the road leading up to it."
Email [email protected] or call the force on 101, select option 2, and ask for Will Lane.
Quote reference 12180200455 when passing on any information.