This invention relates to a system for processing access requests issued from a plurality of access requesting units to a memory. In particular, in a storage system where the buffer storage BS and main storage MS are provided, access is first made to BS based on and access request and if the desired data is not found in BS, access is made to MS. When the desired data is not found in BS and access is then made to MS, acces to BS is carried out based on the next access request from the same access requesting unit in parallel with the access to MS by the first access request.