The South American knifefish Eigenmannia sp. can detect the electric organ discharges (EODs; 250­600 Hz) of conspecifics when they are superimposed over its own EOD. This study investigates the minimum frequency difference necessary for such signal perception, using the application of sine-wave stimuli. Electrosensory stimulus-intensity thresholds were determined for trained fish using stimuli associated with food rewards. These sine-wave stimuli were 'clamped' to the EOD frequency of the fish. Electrosensory thresholds were also determined for the spontaneous jamming avoidance response (JAR; a change in EOD frequency evoked by a stimulus of sufficiently similar frequency), in this case using unclamped stimuli. Over the wide frequency range investigated (0.3­3.01 times EOD frequency), the lowest stimulus-intensity thresholds of 0.6 µV cm-1 (peak-to-peak) (0 dB) at a water conductivity of 100 µS cm-1 were found close to (but not exactly at) the EOD fundamental frequency. At exact frequency identity between the EOD and the stimulus, the stimulus-intensity response threshold rose abruptly by more than 10 dB compared with slightly higher or lower stimulus frequencies. A similar 'needle-like' threshold increase was found at exactly two and three times the EOD frequency, but neither at harmonic ratios between stimulus and EOD frequency that represent fractions (e.g. at 5:4=1.25, 4:3=1.33, 3:2=1.5 or 5:3=1.67 times EOD frequency) nor at subharmonics such as half or two-thirds of the EOD frequency. The steepest increase of stimulus-intensity response threshold was in the range 0.998­1.002 times EOD frequency, corresponding to a threshold change, or electrosensory filter slope, of 5000 dB per octave. For the spontaneous JAR, a similar stimulus-intensity threshold increase was observed when EOD frequency equalled stimulus frequency. Because of the longer rise time for the stimulus amplitude (400 ms rather than 35 ms) the stimulus intensity threshold was higher (up to 32 dB; mean, 20 dB) than in the other experiments (up to 15 dB; mean, 13 dB). A difference in frequency between the EOD and the applied stimulus as small as 1 Hz (that is, 0.2 % of the EOD frequency) was sufficient for good signal perception in Eigenmannia sp. The JAR appears to be useful in avoiding insensitivity at exact integer harmonics of the EOD frequency.