The threshold of a short interaurally phase-inverted probe tone (20 ms, 500 Hz, S pi) was obtained in the presence of a 750-ms noise masker that was switched after 375 ms from interaurally phase-inverted (N pi) to interaurally in-phase (No). As the delay between probe-tone offset and noise phase transition is increased, the threshold decays from the N pi S pi threshold (masking level difference = 0 dB) to the No S pi threshold (masking level difference = 15 dB). The decay in this "binaural" situation is substantially slower than in a comparable "monaural" situation, where the interaural phase of the masker is held constant (N pi), but the level of the masker is reduced by 15 dB. The prolonged decay provides evidence for additional binaural sluggishness associated with "binaural forward masking." In a second experiment, "binaural backward masking" is studied by time reversing the maskers described above. Again, the situation where the phase is switched from No to N pi exhibits a slower transition than the situation with constant interaural phase (N pi) and a 15-dB increase in the level of the masker. The data for the binaural situations are compatible with the results of a related experiment, previously reported by Grantham and Wightman [J. Acoust. Soc. Am. 65, 1509-1517 (1979)] and are well fit by a model that incorporates a double-sided exponential temporal integration window.