Provided are a computer program product, system, and method for caching data in a storage system having multiple caches. A sequential access storage device includes a sequential access storage medium and a non-volatile storage device integrated in the sequential access storage device, received modified tracks are cached in the non-volatile storage device, wherein the non-volatile storage device is a faster access device than the sequential access storage medium. A spatial index indicates the modified tracks in the non-volatile storage device in an ordering based on their physical location in the sequential access storage medium. The modified tracks are destaged from the non-volatile storage device by comparing a current position of a write head to physical locations of the modified tracks on the sequential access storage medium indicated in the spatial index to select a modified track to destage from the non-volatile storage device to the storage device.