Amplitude modulation (AM) and frequency modulation (FM) provide crucial auditory information. If FM is encoded as AM, it should be possible to give a unified account of AM and FM perception both in terms of response consistency and performance. These two aspects of behavior were estimated for normal-hearing participants using a constant-stimuli, forced-choice detection task repeated twice with the same stimuli (double pass). Sinusoidal AM or FM with rates of 2 or 20 Hz were applied to a 500-Hz pure-tone carrier and presented at detection threshold. All stimuli were masked by a modulation noise. Percent agreement of responses across passes and percent-correct detection for the two passes were used to estimate consistency and performance, respectively. These data were simulated using a model implementing peripheral processes, a central modulation filterbank, an additive internal noise, and a template-matching device. Different levels of internal noise were required to reproduce AM and FM data, but a single level could account for the 2- and 20-Hz AM data. As for FM, two levels of internal noise were needed to account for detection at slow and fast rates. Finally, the level of internal noise yielding best predictions increased with the level of the modulation-noise masker. Overall, these results suggest that different sources of internal variability are involved for AM and FM detection at low audio frequencies.