1. A data backup method for a computer system having a central processing unit for performing a plurality of tasks in parallel, a multiple memory including at least two memory means and a control means for managing said memory means, and a data backup memory for backup of data stored in said memory means of said multiple memory, said method comprising the computer-executed steps of: storing an operation mode of each said memory means of said multiple memory into a table previously provided in said multiple memory; when said central processing unit issues a maintenance task for evacuating data from said memory means of said multiple memory to said backup memory, said control means performs the steps of: comparing an operation mode assigned to said maintenance task with said operation mode stored in said table of each said memory means of said multiple memory; changing the operation mode of at least one memory means to said operation mode assigned to said maintenance task in accordance with a result of said comparing step; and executing said maintenance task with respect to said memory means whose operation mode has been changed.