When cerebellar Purkinje cells are depolarized with a constant current pulse injected at the soma, complex spike discharge patterns are observed (Llinas and Sugimori 1980b). A computer model has been constructed to analyze how the Purkinje cell ionic conductance identified to date interact to produce the observed firing behavior. The kinetics of voltage-dependent conductance used in the model were significantly simpler than Hodgkin-Huxley kinetics, which have many parameters that must be experimentally determined. Our simplified scheme was able to reproduce the complex nonlinear responses found in real Purkinje cells. A similar approach could be used to study the wide variety of neurons found in different brain regions.