Provided are a computer program product, system, and method for managing caching of extents of tracks in a first cache, second cache and storage device. A determination is made of an eligible track in a first cache eligible for demotion to a second cache, wherein the tracks are stored in extents configured in a storage device, wherein each extent is comprised of a plurality of tracks. A determination is made of an extent including the eligible track and whether second cache caching for the determined extent is enabled or disabled. The eligible track is demoted from the first cache to the second cache in response to determining that the second cache caching for the determined extent is enabled. Selection is made not to demote the eligible track in response to determining that the second cache caching for the determined extent is disabled.