Method, system, and program for establishing and maintaining a point-in-time copy

Provided are a method, system, and program for establishing a point-in-time copy. Input/Output (I/O) requests to tracks identified as source tracks and corresponding target tracks in a point-in-time copy relationship are suspended until the point-in-time copy relationship is established. At least one data structure providing information on the source tracks and corresponding target tracks in the point-in-time copy relationship is generated, wherein the point-in-time copy relationship is established before data at the source tracks is copied to the target tracks and before source tracks in cache at the point-in-time are destaged to storage.