Many natural sounds, including speech and animal vocalizations, involve rapid sequences that vary in spectrum and amplitude. Each sound within a sequence has the potential to affect the audibility of subsequent sounds in a process known as forward masking. Little is known about the neural mechanisms underlying forward masking, particularly in more realistic situations in which multiple sounds follow each other in rapid succession. A parsimonious hypothesis is that the effects of consecutive sounds combine linearly, so that the total masking effect is a simple sum of the contributions from the individual maskers. The experiment reported here tests a counterintuitive prediction of this linear-summation hypothesis, namely that a sound that itself is inaudible should, under certain circumstances, affect the audibility of subsequent sounds. The results show that, when two forward maskers are combined, the second of the two maskers can continue to produce substantial masking, even when it is completely masked by the first masker. Thus, inaudible sounds can affect the perception of subsequent sounds. A model incorporating instantaneous compression (reflecting the nonlinear response of the basilar membrane in the cochlea), followed by linear summation of the effects of the maskers, provides a good account of the data. Despite the presence of multiple sources of nonlinearity in the auditory system, masking effects by sequential sounds combine in a manner that is well captured by a time-invariant linear system.