In a nonvolatile semiconductor memory device capable of the storage of multivalued data, fast writing can be realized with high reliability. In such a nonvolatile semiconductor memory device for storing multivalued information in one memory cell by setting a plurality of threshold voltages of data, writing of data having one threshold voltage that is the remotest to an erased state is performed prior to writing of the data having the other threshold voltages (write #1). Writing of the data having the other threshold voltages is then sequentially performed within groups of threshold voltages, starting from the nearer threshold voltage to the erased state within each group. When writing each of the data having the other threshold voltages, writing of the data is performed to a memory cell beginning with those groups having the remoter threshold voltages from the erased state.