Hodgkin and Huxley equations were modified to include the properties of an external diffusion barrier separated from the axolemma by a thin periaxonal space in which potassium ions accumulate as a function of membrane activity. Further modifications in the equations took into account new values for gK and new functions for alphan, betan, alphah, and betah derived from voltage clamp experiments on Loligo pealei giant axons. Equations were solved on a PDP-11 computer using the Gear predictor-corrector numerical method. In comparison with the original Hodgkin and Huxley equations, the modified equations for membrane potentials gave: 1) more accurate representations of the falling and undershoot phases of the membrane action potential, 2) more accurate representation of thresholds and latencies, 3) increases in the periaxonal space potassium ion concentration, Ks, of about 1 mM/impulse, 4) proper predictions of the time course and magnitude of either undershoot decline or periaxonal potassium ion accumulation during trains of membrane action potentials elicited by repetitivie short duration stimuli, and5) a somewhat more accurate representation of adaptation (finite train and nonrepetitive responses) during long duration constant current stimulation.