The mathematical theory of stochastic point processes in its probabilistic and statistical aspects is applied to nerve-impulse sequences. Mathematical results are extended and illustrated through the application of statistical techniques to the results of computer experiments on simulated nerve cells. Statistical techniques at several levels of complexity are used in the analysis of single stationary spike trains. A set of techniques is presented for analyzing two spike trains simultaneously in the presence and absence of stimulation. It is shown how to test for independence of the two cells and to diagnose the sources of dependence when found. The effects of trends in the data on the computational results are discussed and illustrated.