It happened at a set of traffic lights.
Police have been conducting extra patrols and house to house enquiries, after the fight left one man in hospital.
It happened on Hollow Way Road, at the junction of Garsington Road and Oxford Road, on Saturday evening.
The occupants of a Ford Fiesta and a BMW were involved.
Two men sustained head injuries and were taken to the John Radcliffe, where one of them remains.
Thames Valley Police is appealing for information.
Investigating officer, Detective Constable Nicola Clark of Force CID based at St Aldates Police Station, said: "I am appealing to anyone who has information or witnessed this altercation, especially if you have CCTV, dashcam or mobile phone footage of the incident.
"If you have any information please contact police by calling 101 or visiting your nearest police station and quoting reference 43180206437.
"A thorough investigation is underway, with our officers conducting house to house enquiries, extra patrols in the area, forensic enquiries and obtaining and reviewing CCTV."