1. A storage system, comprising: multiple channel adapters each for performing data communication with one or more host devices; multiple storage devices for storing data; multiple storage adapters each for performing data communication with the multiple storage devices; a main cache memory for temporarily storing data exchanged between the multiple channel adapters and the multiple storage adapters; and a connection network for connecting the multiple channel adapters and the multiple storage adapters to the main cache memory, each of the multiple channel adapters having: a processor for controlling the data communication with the host devices; and a local cache memory for temporarily storing data accessed by the host devices, wherein, when the processor within each of the channel adapters receives write-data and a write-request with respect to the write-data from the host device, the write data is written in the local cache memory, directory information for locating the storage area of the write-data in the storage device is stored, a response to the write-request is sent to the host device, and the write-data is transferred from the local cache memory to the main cache memory through the connection network such that the write-data can be written in the storage device by the storage adapter.