1. We recorded single unit activity from individual primary electrosensory afferent axons in the posterior branch of the anterior lateral line nerve of gymnotid weakly electric fish, Apteronotus leptorhynchus. We analyzed the responses of P-type (probability-coding) afferent fibers to externally applied amplitude step changes in the quasi-sinusoidal transdermal potential established by the fish's own electric organ discharge (EOD). 2. In response to AM step increases in transdermal potential, the firing rate of P-type afferents exhibited an abrupt increase followed by an initially rapid and subsequently more gradual decay back toward the baseline level. Afferent responses continued to adapt slowly throughout the duration of prolonged step stimuli lasting > 100 s. The time course of sensory adaptation was similar for all units tested. 3. We introduce a new functional form for describing the time course of sensory adaptation in which the change in firing rate delta r decays logarithmically with time: delta r(t) = A/[B In (t) + 1]. This logarithmic form accurately describes the adaptation time course of P-type afferents over five decades in time, from milliseconds to hundreds of seconds, with only two free parameters. Using a nonlinear least-squares fitting technique, we obtained a mean value of the parameter B, which characterizes the adaptation time course, of 0.149 +/- 0.028 (mean +/- SD, n = 49). 4. We compare logarithmic fits with traditional multiexponential and power law forms and demonstrate that the logarithmic form yields a better characterization of P-type afferent responses. This analysis helps explain the variability in previously reported adaptation time constants, which have ranged from 0.2 to 3.4 s, in gymnotid P-type afferents. 5. We tested the linearity of P-type afferent responses using positive and negative AM steps of varying amplitudes. Aside from nonlinearities associated with rectification (firing rates cannot be negative) and saturation (firing rates cannot exceed the EOD frequency), we found that P-type afferent responses scaled linearly with stimulus amplitude. 6. Based on the observed linearity, we predict the frequency domain response characteristics of P-type afferents and find that the predicted gain and phase are in good agreement with experimental measurements using sinusoidal AM stimuli over a range of AM frequencies from 1 to 100 Hz. Thus the logarithmic parameterization of the step appears to accurately capture the response dynamics of P-type afferents over a wide range of behaviorally relevant AM frequencies. 7. We conclude that the temporal filtering properties of pyramidal cells in the medullary electrosensory nucleus, the electrosensory lateral line lobe (ELL), need to be reevaluated in light of the logarithmic adaptation time course in the periphery, and we discuss implications for the role of P-type afferents in driving a feedback gain control mechanism that regulated ELL pyramidal cell responsiveness.