Bruce and Priscilla Wetherill, both 84, have described the brief encounter, which happened between Gainford and Barnard Castle, as “frightening”.
They pair say they saw something strange in the sky as they drove past a wooded area near Arlaw Banks.
Mrs Wetherill said: “We saw this thing heading towards us – it was coming right at us and was as low as the car and huge. It was very frightening.
“Bruce kept driving but we both ducked down, expecting it to hit us. I thought, ‘This is it, we’ve had it’.”
The Wetherills said the UFO, which was shaped like a flying saucer, was dark on top but glowed underneath and made no sound.
At the last moment, it lifted up and narrowly missed the car, they said. Mr Wetherill said: “It was an amazing thing – it came so close to us that I thought it was going to crash on us.
“We were waiting for an explosion, but then it disappeared. It all took place in a split-second.”
The 84-year-old said the UFO disappeared into the sky.
“I’m a realist, but I know what I saw and it was unbelievable.
“If I lived to 200 I would never see anything like it again,” Mr Wetherill said.
Mrs Wetherill, who is also convinced about what she saw, said the UFO had steel-like tentacles hanging down.
The couple said the flying saucer came so close that they expected to see scratches on the roof of their vehicle.
But when they investigated, there were none.
Mrs Wetherill said that since the encounter, she has been too scared to drive past the spot at night.
The couple said the incident happened two years ago but they wanted to come forward after a spate of recent UFO sightings in Teesdale, as reported in last week’s Teesdale Mercury.