The management of Wantage Civic Hall is to be transferred to a not-for-profit trust organisation by April next year.
But the Vale of White Horse District Council, which is to do the same for the Guildhall in Abingdon, said users of the buildings should notice no difference.
The decision to transfer the management was taken as part of the district council's budget for the coming year, in which it had to make savings of £1m.
Nick Garnett, the council's assistant director of leisure, said a not-for-profit trust-based organisation would be able to take advantage of savings on business rates which the council was not entitled to. Transferring the management would also offer VAT benefits.
Mr Garnett said the aim was that services presently provided at the buildings would be retained.
The move follows the successful takeover of the running of leisure centres at Wantage, Faringdon and Tilsley Park, in Abingdon, by South Oxfordshire Leisure Limited (SOLL).
Joyce Hutchinson, the council's portfolio holder for leisure, culture and sport, said: "Hopefully the only difference people will notice will be that there will be improvements and the buildings will be used much more. They will be more business-managed. We will emphasise that the community use is to be kept."
Melinda Tilley, leader of the Conservative group on the council, said she could appreciate the financial benefits of the transfer, but said it needed to be handled carefully with staff kept fully informed.
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