In one embodiment, storage drive dependent track removal processing logic performs destage tasks for tracks cached in a cache as a function of whether the storage drive is classified as a fast class or as slow class of storage drives, for example. In one embodiment, a destage task configured for a slow class storage drive, transfers an entry for a track selected for destaging from a main cache list to a wait cache list to await destaging to the slow class drive. A destage task configured for a fast class storage drive allows the cache list entry for the selected track to remain on the main cache list while the selected track is being destaged to the fast class storage drive, thereby bypassing the transfer of the entry to a wait cache list. Other features and aspects may be realized, depending upon the particular application.