It happened on the A714 near Glentrool on Saturday afternoon at about 5.30 pm.
A blue Yamaha XJR motorbike and a yellow Ford Eco sport car were involved.
The motorcycle rider and passenger, a 61-year-old man and a 60-year-old woman respectively, were taken to Dumfries and Galloway Royal Infirmary in Dumfries.However, the two people, aged 30 and 31, in the car were uninjured.
Officers are keen to speak to anyone who was in the area around this time and witnessed the crash.Police Constable Liza Murdoch said: “Enquiries are ongoing to establish the full circumstances and I am appealing to anyone who may have seen the vehicles before the crash to get in touch.“We are particularly interested in speaking with the driver of a red van and other motorcyclists, who were seen in the area shortly before the crash.“I am also asking anyone who may have dash-cam footage that could assist our enquiries to contact us.”Anyone who can assist is asked to call Police Scotland on 101, quoting incident number 2939, of Saturday, 10 September, 2022
