1. A method for preventing over-programming of resistive random access (ReRAM) memory cells in a ReRAM memory array comprising: applying a programming voltage in a programming circuit path including a ReRAM memory cell to be programmed; sensing programming current drawn by the ReRAM memory cell while the programming voltage is applied across the ReRAM memory cell by sensing a voltage drop in a bit line in the memory array, the bit line being in the programming circuit path; and increasing a resistance of a circuit element in the programming path as a function of the rise in programming current by reducing a gate drive voltage to at least one MOS transistor in the programming path by an amount that is a function of the voltage drop.