Speech intelligibility is degraded in the presence of a competing talker for cochlear implantees, presumably because of impaired tracking and integration of speech segments glimpsed in the masker valleys. This hypothesis was tested by assessing the intelligibility of periodically-interrupted bisyllables produced by a male and female talker, for normal-hearing listeners and implantees. A 4-Hz square-wave modulator with random phase was used to interrupt bisyllables from each talker. Stimuli were either presented alone (Experiment I) or interleaved (Experiment II: the two talkers were alternated). In Experiment I, the mean identification score for each voice was 88% for normal-hearing listeners and 35% for implantees. In Experiment II, the mean score corresponding to correct identification of both voices was 50% for normal-hearing listeners and 5% for implantees. Implantees identified at least one bisyllable among the two well above chance level but showed difficulties assigning it to the correct talker. This suggests that implantees can make use of partial information, but cannot track and integrate the non-adjacent components of interleaved speech as well as normal-hearing listeners. Additional results obtained with normal-hearing listeners tested with tone-vocoded syllables suggest that impaired tracking/integration for implantees stems from limited reception of spectral and temporal fine structure cues.