To characterize the dependencies of ERPs in lower vertebrates and brain levels upon recent history and sequences of stimuli, trains of flashes were delivered at various frequencies to unanesthetized rays while recording in optic tectum and telencephalon. ERPs to repetitive stimuli cannot be understood in terms of simple refractoriness and recovery. Processes must be invoked such as simultaneous excitation and suppression, facilitation and its opposite, rebound and induced rhythms, each with development and decay times and nonlinearities. Some of these processes are uncovered by omitting a stimulus from a train. Omitted stimulus potentials (OSPs) act as though the brain expects a stimulus within 5-7 ms of the interstimulus interval (ISI) of the train. Very few ISIs suffice. The effect upon VEP form and duration of the number of stimuli in short trains, before the steady state response (SSR) is established, is complex. Alternation of the amplitude of successive VEPs (1 large every 2 VEPs, 1 in 3, 1 in 4) is one indication of complexities in the SSR. OSPs also alternate. A single extra stimulus interpolated into a regular train causes distinct effects according to its position. Sharp discontinuities in these effects appear with <5 ms shifts. Total power of the SSR decreases with stimulation frequency but there is a large peak of increased power at 7 Hz and another at 12 Hz. Induced rhythms are a labile, late phase of OSPs as well as of rested VEPs and of the OFF response to a long light pulse. Jittered ISI experiments show that the apparent expectation of the OSP is little affected and that the intervals in the last few hundred milliseconds are most influential. The OSP studied here (ISI <0.5 s)is quite different from that so far studied in human subjects (ISI >1s). We predict further similarities when each taxon is tested in the other ISI range. A major category of response characteristics, besides sensitivity, receptive fields and recovery times, is dependence upon recent history of iterative events, including intervals, delays, omissions and perhaps multiple facilitating and forgetting time constants. The variables examined parametrically in this study are only some of those available. Such dynamical characteristics are important neglected properties of afferent systems at each level