Two aspects of neuronal function were investigated: the passive electrical properties of neuronal membranes and the initiation of action potentials. The passive electrical properties of a neurone, together with its morphology, determine the efficiency of synaptic current transfer to the impulse initiation zone. A general analysis was made of the problems of estimating the electrical properties of a neurone from the measured input impedance with the aid of equations for the input impedance. These equations were used to quantify the error resulting from an idealization of the neurones structure. Furthermore, frequency and time domain methods for electrotonic parameter estimation were contrasted and frequency domain methods were shown to be less susceptible to error. Frequency domain methods were applied to the problem of estimating the electrotonic parameters of some identified neurones of the garden snail. The membrane time constants for the group of neurones studied had an average value of 43 ms. The nonlinear properties of snail neurones were characterised by measuring the harmonic content of the voltage response to a sinusoidal current input. The model so deduced accounted for the response of neurones for inputs with peak-to-peak amplitudes up to 2 nA, but the form of the input showed a strong dependence on the DC bias of the input. In the second part of this thesis stochastic and deterministic signals were used to characterise and model the dynamics of spike initiation. Neurones were stimulated with Gaussian white noise current signals. Records of the action potentials evoked together with the input noise allowed measurement of the characteristics of the current trajectories that lead to the initiation of action potentials. These records were analysed in the framework of Wiener's theory of nonlinear systems to obtain a model of the current-to-spike transformation. The models were similar in form to that of a low-pass filler in cascade with a threshold device and predicted 60 to 80% of the observed action potentials. The spiking behaviour evoked by step current inputs was contrasted with that produced by Gaussian white noise and the dynamics of the neurone were shown to depend on the form of the input used.