In many mammals, upward-sweeping frequency-modulated (FM) sounds (up-chirps) evoke larger auditory brainstem responses than downward-sweeping sounds (down-chirps). To determine if similar effects occur in FM echolocating bats, auditory evoked responses (AERs) in big brown bats in response to up-chirps and down-chirps at different chirp durations and levels were recorded. Even though down-chirps are the biologically relevant stimulus for big brown bats, up-chirps typically evoked larger peaks in the AER, but with some exceptions at the shortest chirp durations. The up-chirp duration that produced the largest AERs and the greatest differences between up-chirps and down-chirps varied between individual bats and stimulus levels. Cross-covariance analyses using the entire AER waveform confirmed that amplitudes were typically larger to up-chirps than down-chirps at supra-threshold levels, with optimal durations around 0.5-1 ms. Changes in response latencies with stimulus levels were consistent with previous estimates of amplitude-latency trading. Latencies tended to decrease with increasing up-chirp duration and increase with increasing down-chirp duration. The effects of chirp direction on AER waveforms are generally consistent with those seen in other mammals but with small differences in response patterns that may reflect specializations for FM echolocation.