1. A storage subsystem comprising: plural storage units; and a storage control unit that is connected to a central processing unit and has an internal cache memory for temporarily storing data exchanged between said central processing unit and said storage units, wherein: said storage subsystem is connected to said central processing unit by an I/O interface protocol by which said central processing unit issues I/O requests consisting of a chain of plural commands and data to said storage control unit asynchronously with responses from said storage control unit; said storage control unit has a means that decides order of processing said plural commands and data from said central processing unit independently of the order they were received, and executes said commands; and said plural storage units are under control of said storage control unit.