Afterhyperpolarization (AHP) following single or short trains of spikes in rubrospinal neurones (RN neurones) of the cat has been studied with intracellular recording techniques. The AHP amplitude was potential dependent; it increased with depolarization and decreased with hyperpolarization and had an extrapolated reversal potential about 20 mV below resting membrane potential. The AHP was associated with an increase in the membrane conductance and it was concluded that the AHP is primarily caused by an increase in membrane conductance to potassium ions. The time course of the conductance change underlying the AHP was measured with short current pulses and calculated from the AHP voltage. The AHP following a single spike was conditioned at different interspike intervals by a preceding spike (or several spikes). In many RN neurones the AHP (conductance) following a spike added approximately linear to that generated by a preceding spike. In most cells, however, the AHP following a spike was instead depressed by a preceding spike. The summation of AHPs increased progressively, while the depression appeared to be already maximal with one preceding spike. The depression was then approximately constant for interspike intervals less than the AHP duration. It will be shown in a following paper that these properties of the AHP are reflected in the behaviour of the repetitive discharge evoked by constant current pulses in the same neurones.