The serious accident happened at Culmore Road last Sunday, October 14.
Strand Road-based officer Constable McCausland said: “At around 4.25 pm, it was reported that a white Volkswagen Golf and a grey BMW X1 were involved in the collision.
“Northern Ireland Ambulance Service attended the scene and a female passenger in the VW Golf in her 70’s was taken to hospital for treatment.
“Her condition is described as serious but stable.
“A male driver in his 70’s of the VW Golf was also taken to hospital for injuries that are not believed to be life threatening.
“Enquiries are continuing and we would appeal to anyone who witnessed the incident or who has dashcam footage of the vehicles prior to the incident to contact police on 101 quoting reference number 968 14/10/18.”