This study investigates how the phase curvature of the auditory filters varies with center frequency (CF) and level. Harmonic tone complex maskers were used, with component phases adjusted using a variant of an equation proposed by Schroeder [IEEE Trans. Inf. Theory 16, 85-89 (1970)]. In experiment 1, the phase curvature of the masker was varied systematically and sinusoidal signal thresholds were measured at frequencies from 125 to 8000 Hz. At all signal frequencies, threshold differences of 20 dB or more were observed between the most effective and least effective masker phase curvature. In experiment 2, the effect of overall masker level on masker phase effects was studied using signal frequencies of 250, 1000, and 4000 Hz. The results were used to estimate the phase curvature of the auditory filters. The estimated relative phase curvature decreases dramatically with decreasing CF below 1000 Hz. At frequencies above 1000 Hz, relative auditory-filter phase curvature increases only slowly with increasing CF, or may remain constant. The phase curvature of the auditory filters seems to be broadly independent of overall level. Most aspects of the data are in qualitative agreement with peripheral physiological findings from other mammals, which suggests that the phase responses observed here are of peripheral origin. However, in contrast to the data reported in a cat auditory-nerve study [Carney et al., J. Acoust. Soc. Am. 105, 2384-2391 (1999)], no reversal in the sign of the phase curvature was observed at very low frequencies. Overall, the results provide a framework for mapping out the phase curvature of the auditory filters and provide constraints on future models of peripheral filtering in the human auditory system.