Since a nonvolatile RAM allows random reading and writing operations, an erasing mode is unnecessary. From the system side, however, it is desirable to have the erasing mode because of its nonvolatile characteristic. Moreover, the erasing operation is desirably carried out at high speed with low power consumption. Therefore, memory cell arrays COA and DTA containing a plurality of memory cells MC each having a magnetoresistive element are provided, a series of data is written to the memory cell arrays COA and DTA, and at the time of erasing, an erasing operation is carried out by writing predetermined data only to the memory cell array COA.