The electric organ discharge (EOD) of the South American knifefish Eigenmannia sp. is a permanently present wave signal of usually constant amplitude and frequency (similar to a sine wave). A fish perceives discharges of other fish as a modulation of its own. At frequency identity (∆F = 0 Hz) the phase difference between a fish's own electric discharge and that of another fish affects the superimposed waveform. It was unclear whether or not the electrosensory stimulus- intensity threshold as behaviourally determined depends on the phase difference between a fish's own EOD and a sine-wave stimulus (at ∆F = 0 Hz). Also the strength of the jamming avoidance response (JAR), a discharge frequency shift away from a stimulus that is sufficiently close to the EOD frequency, as a function of phase difference was studied. Sine-wave stimuli were both frequency-clamped and phase-locked to a fish's discharge frequency (∆F = 0Hz). In food-rewarded fish, the electrosensory stimulus-intensity threshold depended significantly on the phase difference between a fish's discharge and the stimulus. Stimulus-intensity thresholds were low (down to 3 µV/cm, peak-to-peak) when the superimposed complex wave changed such that the shift in zero-crossings times relative to the original EOD was large but amplitude change minimal; stimulus-intensity thresholds were high (up to 16.9 µV/cm, peak-to-peak) when the shift in zero-crossings times was small but amplitude change maximal. Similar results were obtained for the non-conditioned JAR: at constant supra-threshold stimulus intensities and ∆F = 0 Hz, the phase difference significantly affected the strength of the JAR, although variability between individuals was higher than that observed in the conditioned experiments.