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1. It has been suggested that spontaneous quantal release of transmitter at the neuromuscular junction is a Poisson process. One logical argument against accepting the Poisson hypothesis is that so far relatively few intervals between miniature end-plate potentials (min.e.p.p.s) have been studied in any single experiment. Release is known to occur from many sites on the nerve terminal, so many intervals must be studied before drawing any conclusions about the timing of release from the individual sites. Moreover, the statistical methods that have been used are relatively insensitive to deviations from Poisson predictions.

2. The Poisson hypothesis is evaluated with respect to three major criteria:

(a) The fit to the exponential distribution is analysed by five goodness of fit tests which were applied to eleven sets of data, showing that it is unlikely that the data sets were generated by an exponential distribution.

(b) The independence of intervals is assessed in two ways. First, the autocorrelogram of intervals is constructed. This shows an excess of significant positive correlations beyond the 5% limits of the Poisson expectation. Secondly, the unsmoothed power spectrum is calculated, and compared to the Poisson prediction by means of the modified mean test. Again, most sets deviate significantly from the Poisson expectation. It is unlikely that the intervals are independent.

(c) The possibility of simultaneous occurrences is evaluated by construction of the amplitude histogram of min.e.p.p.s. In all sets the Poisson prediction for the frequency of multiples of the unit height was exceeded by the empirical data sets. The over-all conclusion is that the process which generates spontaneous releases is unlikely to be Poisson.