1. A storage system comprising: a plurality of disk units; and a controller coupled to the plurality of disk units, wherein the controller includes therein: a plurality of first an adaptor, each of which is to be coupled to a computer and receives an access command from the computer; a plurality of second adaptors coupled to the plurality of disk units and controlling data input/output to/from the plurality of disk units; a shared memory for storing control data transmitted between the plurality of first adaptors and the plurality of second adaptors to execute operations according to an access command from the computer; and a cache memory for storing data transmitted between the plurality of first adaptors and the plurality of second adaptors, wherein when a first adaptor receives an access command from the computer, the first adaptor stores control data in the shared memory, and said data requested to be accessed in the access command are transmitted via the cache memory between the first adaptor and a second adaptor, the first adaptor executes operations according to the control data stored in the shared memory, wherein each of the plurality of first adaptors includes: a port unit for receiving an access command from the computer; a plurality of processor units, each of which has a memory area used for storing a message to be communicated among the port unit and the plurality of processor units and executes operations for data transmission between the first adaptor and the cache memory according to the message stored in the memory area; wherein when a second one of the processor unit is taking over the processing of a first one of the processor units, a protocol unit of the port unit temporarily stores the access command and then transfers the access command to the second processor unit after the second processor unit takes over the processing of the first processor unit.