Echolocating bats (Eptesicus fuscus) can detect jitter in the arrival‐time of sonar echoes as small as 500 ns. These bats could thus detect fluttering motions of prey resulting in displacements in range as small as 100–200 μm The range‐axis acoustic image of a planar target corresponds to the half‐wave‐rectified crosscorrelation function between the bat's broadband FM sonar transmissions and echoes.Eptesicuscan perceive echo phase information as would be encoded by phase‐locked discharges to excitatory half‐cycles of transmission and echo waveforms, which cover the frequency span from 25 to 100 kHz. Ambiguity in echo arrival‐time perception occurs for time‐separations corresponding to small integer multiples of average signal periods. The time‐domain neural crosscorrelator required here for extracting periodicity in sonar sounds and echoes has the desirable properties of recovering harmonic‐interval or “missing fundamental” periods in complex sounds and extraction and representation of periodicity information potentially for pitch perception. The data indicate that phase‐coding occurs in the auditory systems of bats at very high stimulus frequencies.