1. A nonvolatile semiconductor memory device having nonvolatile memory cells, each of said memory cells comprising a semiconductor substrate of one type of electric conduction, a pair of source and drain regions of the opposite type of electric conduction formed in said semiconductor substrate, an electric charge-capturing film formed on a channel region between said pair of source and drain regions, and a gate electrode formed on said charge-capturing film and working as a control electrode; wherein said electric charge-capturing film has a multi-layer structure in which at least four insulating films and at least three electric charge accumulation films are alternatingly laminated one upon the other, the lowermost insulating film among said at least four insulating films is formed as a gate-insulating film, at least one electric charge accumulation film among said three electric charge accumulation films includes a nitride film, a plurality of different threshold voltages are set to said three electric charge accumulation films to correspond to their electric charge-capturing states, and at least four kinds of memory states are specified depending upon said plurality of threshold voltages.