Provided are a method, system, and program for migrating source data to target data. A write request is received to write application data to source data not yet migrated to the target data. Information is generated for the write request indicating the source data to which the application data is written. The application data is written to the source data. A request is received to migrate source data to target data and indication is returned to retry the request to migrate in response to determining that the requested source data to migrate overlaps source data indicated in the generated information for one write request.