Northumbria Police said two men in a Transit van claiming to know and live near Mr Coates had pulled up and taken the bicycle after the first collision.
But the bike is now missing and police are appealing for witnesses.
The police force said the men, in a grey van, "looked as if they had just finished work".
Mr Coates was flown in nine minutes to James Cook Hospital, in Middlesbrough, by the Great North Air Ambulance.
The service said it had been unable to land at a hospital in Newcastle because of snow.
Officers questioned the driver of the car which struck Mr Coates, of West Herrington, but no arrests were made.
http://www.sun-fm.com/news/local/801267/cyclist-dies-in-sunderland-accident/
A cyclist has been killed as he swapped details with a driver following an accident in Sunderland.
Stan Coates from West Herrington was involved in a minor collision in Burdon Lane in the Ryhope area on Friday.
As the 55 year old recovered from that, he was hit by another car.
Police want to trace two men in a gray transit van who offered to take the bike home just before the second crash - the cycle hasn't been returned.
http://www.bbc.co.uk/news/uk-england-tyne-20114930
Northumbria Police said two men in a Transit van claiming to know and live near Mr Coates had pulled up and taken the bicycle after the first collision.
But the bike is now missing and police are appealing for witnesses.
The police force said the men, in a grey van, "looked as if they had just finished work".
Mr Coates was flown in nine minutes to James Cook Hospital, in Middlesbrough, by the Great North Air Ambulance.
The service said it had been unable to land at a hospital in Newcastle because of snow.
Officers questioned the driver of the car which struck Mr Coates, of West Herrington, but no arrests were made.