Provided are a method, system and program for processing complexes to access shared devices. A lock to a plurality of shared devices is maintained and accessible to a first and second processing systems. The first processing complex determines a first delay time and the second processing complex determines a second delay time. The first processing complex issues a request for the lock in response to expiration of the first delay time and the second processing complex issues a request for the lock in response to expiration of the second delay time.