The association between membrane excitation and alterations in membrane electrical impedance, its dependence on extracellular Na+ and the accompanying transmembrane Na+ fluxes measurable by isotope tracer methods, gave rise to the Na+ hypothesis for the action potential. Here, suprathreshold depolarising stimulation increases the voltage-dependent Na+ membrane conductance. The latter in turn initiates a regenerative cycle of membrane depolarisation and further channel opening, culminating in the action potential upstroke phase. Subsequent action-potential recovery to the resting potential then follows a voltage-dependent Na+ channel inactivation and more gradual K+ channel opening. This hypothesis was tested by voltage-clamp experiments determining the ionic currents required to drive depolarising membrane-potential steps in cephalopod giant axons from the resting to varying test levels. These revealed Na+ and K+ conductances whose voltage-dependences and kinetic properties could be incorporated into a successful mathematical reconstruction of the timecourse and properties of experimentally observed propagating action potentials.