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 adaptors, 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 adapter which 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; a communication line for communicating a message among the port unit and the plurality of processor units; and a data transfer controller, which is coupled to the cache memory and controls data transmission between the first adaptor and the cache memory, and wherein when an access command is received at a port unit of a first adaptor via the communication line, the port unit sends a message to one of the plurality of processor units of the first adaptor which instructs said one of the plurality of processor units to save the access command in the memory area of said one of the plurality of processor units and to distribute to one of the plurality of processor units of the first adaptor operations for data transmission between the first adaptor and the cache memory, said one of the plurality of processor units determines how to distribute to one of the plurality of processor units of the first adaptor the operations based on processing loads of the plurality of processor units of the first wherein the port unit has a transceiver and a protocol unit, and the protocol unit controls an interface protocol with the computer and carries out data transfer operation with the computer via the transceiver as controlled by said one of the plurality of the processor units; wherein the protocol unit has a memory area which stores control information for communication with said one of the plurality of the processor units in response to a relative quantity of said one of the plurality of the processor units as a communication means with the plurality of the processor units, and the memory area also stores a plurality of outbound message inpointers each corresponding to one of the plurality of processor units respectively, and a plurality of inbound message outpointers each corresponding to one of the plurality of processor units respectively; wherein the memory area of each one of the plurality of processor units is configured with outbound message storing areas each corresponding to one of the plurality of processor units respectively, outbound message outpointers storing areas each corresponding to one of the plurality of processor units respectively, inbound message storing areas each corresponding to one of the plurality of processor units respectively, inbound message inpointers storing areas each corresponding to one of the plurality of processor units respectively, and data information storing areas each corresponding to one of the plurality of processor units respectively.