Provided are a method, system, and program for processing a request to update a file in a file system with update data. The update request to a target file that is directed to the file system is processed, wherein the target file is in a mirror copy relationship with a mirror file. A determination is made as to whether a copy operation from the target file to the mirror file is in progress and whether bytes to update in the target file have been copied to the mirror file in response to determining that the copy operation is in progress. The update data is copied to the bytes to update in the target file in response to determining that the bytes to update have not been copied to the mirror file, wherein the update data is subsequently copied to the mirror file during subsequent progress of the copy operation.