Purpose: The sensitivity to sinusoidal amplitude modulations (SAMs) is reduced when other modulated maskers are presented simultaneously at a distant frequency ( also referred to as modulation detection interference [MDI]). This article describes the results of onset differences between masker and target as a parameter. Method: Carrier frequencies were 1 kHz ( target: 625 ms, 8 Hz SAM) and 2 kHz ( masker: 625 ms, 8 Hz SAM; modulation depth = 1) presented at 25 dB SL for listeners with impaired hearing (n = 8) and at 25 dB SL and 50 dB SL for listeners with normal hearing ( n = 6). Masker was delayed by 0, 125, 250, 500, 625, or 750 ms relative to the target. Results: Sensitivity to SAMs was reduced in both groups by a modulated masker simultaneous presentation. Reducing the temporal overlap (i.e., increasing the onset delay between masker and target) increased the sensitivity to SAMs in the presence of modulated maskers. Conclusion: The gradual reduction in MDI with increasing asynchrony between masker and target suggests that MDI is not solely related to perceptual grouping. Reduced sensitivity to SAMs due to prior stimulation with SAM stimuli ( forward masking), and deficits in across-channel integration, are other factors that may play a role.