A computational device determines whether one or more tasks are waiting for accessing a cache for more than a predetermined amount of time while least recently used (LRU) based replacement of tracks are being performed for the cache via demotion of tracks from a LRU list of tracks corresponding to the cache. In response to determining that one or more tasks are waiting for accessing the cache for more than the predetermined amount of time, in addition to continuing to demote tracks from the LRU list, a plurality of deadlock prevention demotion tasks demote tracks from the cache.