A file system is migrated from a source file server to a target file server in a data network while permitting clients to have concurrent read/write access to the file system. The target file server issues directory read requests and file read requests to the source file server in accordance with a network file access protocol to transfer the file system from the source file server to the target file server. Concurrent with the transfer of the file system from the source file server to the target file server, the target file server responds to client read/write requests for access to the file system. In a preferred embodiment, the target file server maintains a hierarchy of on-line nodes off-line nodes. The online nodes represent file system objects that have been completely migrated, and the offline nodes representing file system objects that have not been completely migrated. The target file server executes a background process that walks through the hierarchy in order to migrate the objects of the offline nodes. When an object has been completely migrated, the target file server changes the offline node for the object to an online node for the object.