Thames Valley Police and South Central Ambulance Service were called to an incident on board a bus at just after 3.15pm yesterday (October 26) near Westgate Shopping Centre.
Thames Valley Police said a man in his 30s had fallen down the stairs and sustained serious injuries.
The bus was in Castle Street at the time of the incident.
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Police said the injured man was taken to hospital where he remains in a critical condition.
The man’s family are aware and the force says an investigation is being conducted into the circumstances.
A spokesperson for Oxford Bus Company said: “On Saturday afternoon a passenger on-board one of our vehicles received emergency medical treatment after an incident in which no-one else was involved.
“Following medical assistance on the vehicle in Oxford the passenger was taken to the John Radcliffe Hospital by ambulance.
“We are assisting the emergency services with their inquiries and have given CCTV footage to the police.
“Our thoughts are with the passenger and his family and we thank everyone who provided medical support.”
Westgate has been approached for comment.