Forty-eight city council seats are up for grabs in 24 new wards, following boundary changes.
The Lib Dem-Green alliance is hoping to hold on to power, while the Labour group wants to take charge of the authority it ran for 20 years until May 2000.
More than 100,000 voters are also being asked whether there should be an elected mayor in Oxford, and if more than 50 per cent say yes, the current way of running the council, with a leader and executive board, will be scrapped.
There are also elections for West Oxfordshire and Cherwell district councils.
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