Disclosed is a flash EEPROM including a voltage lowering circuit therein for lowering an externally applied high voltage serving as a source of an erase pulse to a predetermined voltage in a range in which a tunnel phenomenon sufficiently occurs in memory cells. The voltage lowered by the voltage lowering circuit is converted into a pulse of a small width, and the converted pulse is then applied as an erase pulse to the memory cells. A flash EEPROM including a memory cell array divided into first and second blocks is also disclosed. An erase pulse applying circuit for applying the voltage lowered by the voltage lowering circuit as an erase pulse to the memory cells, and an erase verify circuit for erase verifying are provided for each of the first and second blocks. The erase pulse applying circuit and the erase verify circuit corresponding to the first block and the ones corresponding to the second block are configured to operate independently.