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1. In the retractor unguis muscles of Periplaneta americana and Blaberus giganteus, the rate of spontaneously occurring miniature potentials from nerve-muscle synapses associated with the `white' muscle fibres was greater than that observed in the `red' muscle fibres.

2. In 5% of the intracellular recordings, particularly from the `white' fibres, short `bursts' of relatively high (20-100 sec^-1) rates of m.e.p.p.s occurred infrequently in an unpredictable manner. This bursting phenomenon was not observed in extracellular recordings of the miniature potential discharge.

3. Rigorous statistical analyses indicated that the spontaneous mode of transmitter release at cockroach retractor unguis muscle fibres was predictable by the negative binomial theorem with a 90% reliability.

4. Perfusion of nerve-muscle preparations with high Mg²⁺ salines resulted in low spontaneous discharge rates which were characterized by a negative binomial distribution.

5. The fit of the data to the negative binomial theorem implied some mutual interaction between those processes responsible for the spontaneous release of transmitter from cockroach nerve terminals.