A modification of the classical procedure of fluctuation analysis is used to measure the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of miniature endplate potentials (MEPPs) at frog cutaneous pectoris neuromuscular junctions treated with black widow spider venom (BWSV). MEPP parameters are determined from the power spectrum of the fluctuating potential and the second (variance), third (skew), and fourth semi-invariants (cumulants) of high-pass-filtered records of the potential. The method gives valid results even when the mean potential undergoes slow changes unrelated to MEPPs and when the MEPP rate is not stationary; it detects changes in the distribution of MEPP amplitudes and corrects for the nonlinear summation of MEPPs. The effects of Ca2+ on BWSV-induced secretion are studied in detail. When Ca2+ is absent, the power spectrum of the fluctuations is shaped like the spectrum of w(t) and secretion is quasi-stationary; (r) rises smoothly to peak values of approximately 1,500/s and then quickly subsides to levels near 10/s. Many relatively small and some "giant" MEPPs occur at the ends of the experiments, and the distribution of MEPP amplitudes broadens. When the effects of this broadening are corrected for, we find that approximately 0.7 X 10(6) MEPPs occurred during the 30 min of intense secretion. Since BWSV depletes nerve terminals of their quanta of transmitter and their synaptic vesicles, this figure is an upper limit for the quantal store in a resting terminal. When Ca2+ is present, the noise spectrum deviates from the spectrum of w(t) and secretion is nonstationary; (r) rises to similar peak values but is sustained at levels near 400/s for up to an hour and at least 1.5 X 10(6) quanta are secreted within this period. Thus, the quantal store must have turned over at least twice under this condition. Data previously obtained at junctions treated with La3+ are corrected for nonlinear summation and for the distribution of MEPP amplitudes. The two corrections roughly compensate each other, and the corrected results confirm the previous conclusion that the number of quanta secreted from La3+-treated terminals during 1 h is not strongly dependent upon the extracellular concentration of Ca2+; approximately 2 X 10(6) quanta are released even when Ca2+ is absent.