The sequence of interspike intervals of the spontaneous activity in denervated electroreceptor organs of the catfish is analysed with several statistical techniques: visual inspection of dot displays, interval histograms, serial correlograms, tests for stationarity and trends, and tests for renewal properties, based on the spectrum of intervals. The interspike interval train of primary afferents can usually be treated as a renewal process. Following denervation, a number of non-renewal properties emerge. The interval histogram of the renewal spike trains can be fitted well with a gamma probability density function; non-renewal cases need a more complex approach. We propose that the stochastic fluctuations in interval duration arise from randomly occurring quantal depolarizations (Stein's model of stochastic neuronal excitation). Two important properties with regard to synaptic transduction are: afferent firing results from capture of a limited number of depolarizing quanta; and the quantal input rate and the threshold for firing appear to be correlated.