The frequency following response (FFR) is a scalp-recorded measure of phase-locked brainstem activity to stimulus-related periodicities. Three experiments investigated the specificity of the FFR for carrier and modulation frequency using adaptation. FFR waveforms evoked by alternating-polarity stimuli were averaged for each polarity and added, to enhance envelope, or subtracted, to enhance temporal fine structure information. The first experiment investigated peristimulus adaptation of the FFR for pure and complex tones as a function of stimulus frequency and fundamental frequency (F0). It showed more adaptation of the FFR in response to sounds with higher frequencies or F0s than to sounds with lower frequency or F0s. The second experiment investigated tuning to modulation rate in the FFR. The FFR to a complex tone with a modulation rate of 213 Hz was not reduced more by an adaptor that had the same modulation rate than by an adaptor with a different modulation rate (90 or 504 Hz), thus providing no evidence that the FFR originates mainly from neurons that respond selectively to the modulation rate of the stimulus. The third experiment investigated tuning to audio frequency in the FFR using pure tones. An adaptor that had the same frequency as the target (213 or 504 Hz) did not generally reduce the FFR to the target more than an adaptor that differed in frequency (by 1.24 octaves). Thus, there was no evidence that the FFR originated mainly from neurons tuned to the frequency of the target. Instead, the results are consistent with the suggestion that the FFR for low-frequency pure tones at medium to high levels mainly originates from neurons tuned to higher frequencies. Implications for the use and interpretation of the FFR are discussed.