Two teenagers were killed when the high-performance sports car they were in span off the road and crashed into a tree.
The £22,000 Lotus Elise belonged to the family of the 18-year-old driver, who police say was properly insured.
The driver and his 17-year-old passenger were from the Eastbourne area. They died at the scene at 9pm on the A26 at Tarring Neville, Newhaven.
The car - which can reach 60mph in six seconds - was travelling north when the driver lost control. It careered off the road and smashed into a tree.
Police were today visiting the teenagers' parents to offer support.
A spokesman said the 125mph car was not registered to the young driver but was owned by the family.
Officers said the victims' names would not be released until all close relatives had been informed.
The driver's parents came across the tragedy when they went looking for their son after he failed to return home.
They were stopped at a police roadblock and realised what had happened when officers told them a Lotus Elise was involved.
Acting Inspector Mark Armstrong, of Bexhill traffic police, said: "The parents were comforted at the scene. This was a dreadful tragedy."
The passenger was later named as Gareth Stew of Northiam Road, Eastbourne.
Police have appealed for witnesses. They particularly want to speak to the occupants of a red Metro who returned to the scene after the crash and spoke to other witnesses.
The busy winding road, which runs from Newhaven to Beddingham, has been the scene of a number of serious accidents.
In August a motorcyclist suffered multiple injuries after his machine crashed into a road sign at Beddingham.
Later the same month two women were taken to hospital after a two-car crash at Heron's Ghyll, near Uckfield.
Anyone with information should contact Sergeant Jim Read at Polegate traffic police on 0845 6070999.
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