This paper presents a method of calculating the spike sequence at the output of the Leaky-Integrator Neuron Model (LIM) in response to an arbitrary input stimulus. The calculations have revealed new properties of the initial transient behavior of the LIM, as well as new constraints upon necessary and sufficient conditions for the appearance of spikes with a fixed phase relation to a periodic input. It is also possible to infer what knowledge about the input stimulus can be obtained from a temporal sequence of spikes at the output of the LIM. In the Discussion, neuronal examples are considered which do not encode the transmitted information as a spike rate, but rather monitor the time of occurence of individual spikes by comparison with a reference signal. This relatively common case is not adequately treated by previous descriptions based on system theory; ways are suggested by which the formalism developed here can be used to describe completely, and understand more fully, the performance of such systems.