The frequency following response (FFR), a scalp-recorded measure of phase-locked brainstem activity, is often assumed to reflect the pitch of sounds as perceived by humans. In two experiments, we investigated the characteristics of the FFR evoked by complex tones. FFR waveforms to alternating-polarity stimuli were averaged for each polarity and added, to enhance envelope, or subtracted, to enhance temporal fine structure information. In experiment 1, frequency-shifted complex tones, with all harmonics shifted by the same amount in Hertz, were presented diotically. Only the autocorrelation functions (ACFs) of the subtraction-FFR waveforms showed a peak at a delay shifted in the direction of the expected pitch shifts. This expected pitch shift was also present in the ACFs of the output of an auditory nerve model. In experiment 2, the components of a harmonic complex with harmonic numbers 2, 3, and 4 were presented either to the same ear ("mono") or the third harmonic was presented contralaterally to the ear receiving the even harmonics ("dichotic"). In the latter case, a pitch corresponding to the missing fundamental was still perceived. Monaural control conditions presenting only the even harmonics ("2 + 4") or only the third harmonic ("3") were also tested. Both the subtraction and the addition waveforms showed that (1) the FFR magnitude spectra for "dichotic" were similar to the sum of the spectra for the two monaural control conditions and lacked peaks at the fundamental frequency and other distortion products visible for "mono" and (2) ACFs for "dichotic" were similar to those for "2 + 4" and dissimilar to those for "mono." The results indicate that the neural responses reflected in the FFR preserve monaural temporal information that may be important for pitch, but provide no evidence for any additional processing over and above that already present in the auditory periphery, and do not directly represent the pitch of dichotic stimuli.