Flash memories (USB portable drives) are close to their miniaturization limits. The ultimate evolution of such devices is believed to exploit different concepts such as electronic phase transitions. Here we show that an electric field can trigger fast resistive switching in the fragile Mott insulators AM(4)X(8) (A = Ga, Ge; M = V, Nb, Ta; X = S, Se). This new type of resistive switching could lead to a new class of resistive random access memory (RRAM) with fast writing/erasing times (down to 50 ns) and resistance ratios Delta R/R of the order of 25% at room temperature.