In order to characterize synaptic transmission at a unitary facilitating synapse in the lobster cardiac ganglion, a new nonlinear systems analysis technique for discrete-input systems was developed and applied. From the output of the postsynaptic cell in response to randomly occurring presynaptic nerve impulses, a set of kernels, analogous to Wiener kernels, was computed. The kernels up to third order served to characterize, with reasonable accuracy, the input-output properties of the synapse. A mathematical model of the synapse was also tested with a random impulse train and model predictions were compared with experimental synaptic output. Although the model proved to be even more accurate overall than the kernel characterization, there were slight but consistent errors in the model's performance. These were also reflected as differences between model and experimental kernels. It is concluded that a random train analysis provides a comprehensive and objective comparison between model and experiment and automatically provides an arbitrarily accurate characterization of a system's input-output behavior, even in complicated cases where other approaches are impractical.