1. Excitatory post-synaptic potentials (e.p.s.p.s) were evoked in cat spinal motoneurones by impulses in single group Ia afferent fibres. The probability density of the fluctuations in peak amplitude of each e.p.s.p. was calculated from the recorded peak amplitude and the probability density of the recording noise. 2. Most e.p.s.p.s fluctuated between different components (i.e. individual e.p.s.p.s of a particular discrete amplitude) with peak amplitudes which were integer multiples of the increment between successive components. The average peak amplitude of this incremental e.p.s.p. was about 90 microV for e.p.s.p.s generated at or near the soma. 3. In general, the probability density of the peak amplitude could not be described using Poisson or binomial distributions. 4. For many e.p.s.p.s the complete time course of each component could be calculated. There was no variability in the amplitude of these components nor in their latency of onset. For some e.p.s.p.s there were differences in the latency and time course of the components. 5. The increments between successive components of e.p.s.p. generated proximally were no larger (at the soma) than the corresponding increments for e.p.s.p.s generated at more distal dendritic sites. 6. These results and those from subsequent papers (Jack, Redman & Wong, 1981; Hirst, Redman & Wong, 1981) reinforce earlier suggestions that each bouton behaves in an all-or-nothing manner with respect to post-synaptic effect, and the probability of failure varies at different boutons arising from the same afferent.