Campaigners have until mid-July to come up with plans to transfer the management of two district libraries to the community.
Bradford Council has given village libraries in Denholme and Addingham a stay of execution as talks continue about handing over the service to volunteers.
A community group in Wrose has also put in a late bid to save its local library.
But the two remaining libraries earmarked for closure – in Wilsden and Heaton – are still on course to close at the end of this month.
Bradford Council announced its plans to close five small libraries earlier this year, in a plan to save the authority £70,000.
The date set for the closures was June 30. The Council is now expected to continue running Addingham and Denholme libraries until July 15.
Addingham and residents initiated talks with the council about running the libraries on a voluntary basis.
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