Threshold measures have been made as a function of the repetition rate and pulse duration of biphasic electrical pulses applied to the cochlea through a cochlear implant (Shannon, 1985). Nonmonotonicities in those data suggest that at least two separate processes are involved in the translation of an electrical stimulus into a threshold perception. This paper presents a phenomenological model which accounts for the key features of the threshold data. The model consists of two parallel processes which are each power-law functions of the instantaneous current amplitude. The output of each process is then integrated with a short time constant (approximately 1-2 ms). The maximum of these two outputs represents the sensory magnitude of that electrical stimulus. Threshold data from 14 patients implanted with three different devices are compared to model predictions over a wide range of pulse durations and pulse rates. Since the model accurately predicts thresholds over such a wide range of stimuli, it is possible that it can predict the threshold of an arbitrary electrical stimulus. This model could be used to construct a speech processor that would convert any acoustic waveform into an equivalent electrical waveform that would preserve threshold relationships.