The purpose of the current study was to investigate the benefits of differences in fundamental frequency (F0) and temporal onset between sentence pairs in four listener groups differing in age and hearing sensitivity. The four groups were: (1) young normal-hearing (YNH) adults; (2) elderly normal-hearing (ENH) adults; (3) elderly hearing-impaired (EHI) adults; and (4) young normal-hearing adults with noise masking (YNM) simulating the hearing loss of the EHI group. Listeners heard two competing sentences separated by F0, temporal onset, or by the combination of both cues. With the increase of F0 or onset separation, speech-identification performance improved in all groups. Differences in F0 and onset between concurrent sentences appeared to substantially reduce the identification errors primarily by reducing the confusion with the competing message. The listener groups did not differ regarding their ability to identify which of the two sentences was the target sentence. For the identification task, overall, the elderly listeners received less benefit from F0 difference and onset asynchrony compared to the young listeners. Given that the EHI listeners performed significantly worse than the young groups (YNH, YNM), but no other groups differed significantly, the combined effects of aging and cochlear pathology appeared to affect competing-speech identification, rather than either aging or reduced audibility alone. Elderly listeners’ benefits from F0 differences were significantly correlated with high-frequency thresholds and age whereas elderly listeners’ benefits from onset asynchrony were significantly correlated with high-frequency thresholds and education level. A general sentence-identification ability of the elderly listeners was also predicted by both high-frequency thresholds and the modality-aspecific, cognitive-related variables, such as education level. This indicates that both age-related peripheral deficits and age-related cognitive deficits contribute to older adults’ difficulty understanding the target message in the presence of a distracter message, even though the audibility of the two messages has been restored.