The Hodgkin-Huxley equation for electrogenesis in the voltage clamped squid giant axon was used to predict the effect of altering maximal Na+ conductance (gNa+max) on the repetitive firing process. The main finding was that increasing gNa+max, without changing any other membrane parameter, reduced the threshold current required to evoke repetitive firing. That is, it rendered the membrane hyperexcitable. Threshold for evoking single action potentials was also affected, but much less so. Other consequences of increasing gNa+max were a decrease in the minimum sustainable rhythmic firing frequency (mRFF), a monotonic increase in firing frequency at any given suprathreshold stimulus intensity, an increase in the current value at which intense depolarizing stimuli block rhythmogenesis, an increase in the maximal sustainable firing frequency using intense currents (MRFF), and the consequent expansion of the dynamic range for stimulus encoding. Thus, the control of gNa+max through the regulation of Na+ channel synthesis and membrane incorporation at sites of rhythmogenesis (e.g. axon hillock-initial segment region, or peripheral sensory endings) is a potential regulatory mechanism for neuronal excitability and stimulus encoding.