Asynchronous local and remote generation of consistent point-in-time snap copies

In accordance with one embodiment, asynchronous local and remote generation of consistent first and second point-in-time snap copy volumes provides for generating in a primary system, a first point-in-time snap copy volume of a primary volume of the primary system, and generating in a secondary system, a second point-in-time snap copy volume utilizing a secondary volume in the secondary system. Synchronizing logic synchronizes the first and second point-in-time snap copy volumes to be consistent with each other as of a particular point-in-time notwithstanding an asynchronous mirror relationship between the primary volume of the primary system and the secondary volume of the secondary system. Other features and aspects may be realized, depending upon the particular application.