A protocol is provided for allocating file locking tasks between primary and secondary data mover computers in a network file server. When there is frequent read access and infrequent write access to a file, a primary data mover grants read locks to the entire file to secondary data movers, and the secondary data movers grant read locks to clients requesting read access. When write access to the file is needed, the read locks to the entire file are released and the read locks granted to the clients are released or expire or are demoted to non-conflicting byte range locks managed by the primary data mover. Concurrent read and write access to the same file is then managed by the primary data mover.