An embodiment non-volatile memory device includes an array of memory cells in rows and columns; a plurality of local bitlines, the memory cells of each column being coupled to a corresponding local bitline; a plurality of main bitlines, each main bitline being coupleable to a corresponding subset of local bitlines; a plurality of program driver circuits, each having a corresponding output node and injecting a programming current in the corresponding output node, each output node coupleable to a corresponding subset of main bitlines. Each program driver circuit further includes a corresponding limiter circuit that is electrically coupled, for each main bitline of the corresponding subset, to a corresponding sense node whose voltage depends, during writing, on the voltage on the corresponding main bitline. Each limiter circuit turns off the corresponding programming current, in case the voltage on any of the corresponding sense nodes overcomes a reference voltage.