A method and apparatus for the programming and erasure of a memory cell made out of floating-gate transistors and to the circuit pertaining thereto is described. It can be applied especially to non-volatile electrically erasable and programmable memories, for example EEPROMs and flash EPROMs. A programming voltage or erasure voltage including a voltage shift equal in value to a reference voltage is produced, followed by a voltage ramp comprising a rising phase followed possibly by voltage plateau, this voltage ramp being shifted in voltage by the value of the reference voltage and being followed, in turn, by a voltage drop. The value of the voltage shift is fixed at an intermediate value that is lower than the value of a so-called tunnel voltage of the memory cell but greater than the supply voltage.