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1. Transmitter release from Mg2+-treated frog neuromuscular junctions can be described by binomial statistics. Good agreement between the observed amplitude-frequency distribution of e.p.p.s. and that predicted by binomial statistics is observed with relatively low concentrations of Mg2+. Conversely, good agreement is found with Poisson predictions when higher concentrations of Mg2+ are used to depress transmission. 2. Binomial analysis at these junctions shows that Mg2+ reduces quantal content (m), the probability of release (p) and to a lesser extent the available stores of transmitter (n). Raising Ca2+ causes an increase in n and p and a small but significant increase in n. K+ increases m and p but not n. 3. During 'frequency-facilitation' (1-6 Hz), e.p.p.s., m and n are increased but p is unaffected. 4. It is concluded that binomial statistics can be used to estimate the quantal parameters of transmitter release and that these parameters can be identified as discrete entities.