The nonlinear, pseudo-periodic permeability (current) of potassium ions through track-etched PETP nuclear membranes has been modelled by a two-parameter logistic map (’crowd model’). D Data obtained by patch clamp procedures for different values of the bath electrolyte concentration has been correlated with a mechanism of transport incorporating structure and morphology of pores in a membrane. Characteristic (singular) behaviour of a current based on the proposed theory is predicted.