A storage subsystem capable of processing time-critical control commands while suppressing deterioration of the system performance to a minimum. When various commands are received in a multiplex manner via the same port from plural host devices, the channel adapter of the storage subsystem extracts commands of a first kind from the received commands. Then, the adapter executes the extracted commands of the first kind with high priority within a given unit time until a given number of guaranteed activations is reached. At the same time, commands of a second kind are enqueued in a queue of commands. After the commands of the first kind are executed as many as the number of guaranteed activations, the commands of the second kind are executed in the unit time.