Hearing thresholds and wave amplitudes measured using auditory brainstem responses (ABRs) to brief sounds are the predominantly used clinical measures to objectively assess auditory function. However, frequency-following responses (FFRs) to tonal carriers and to the modulation envelope (envelope-following responses or EFRs) to longer and spectro-temporally modulated stimuli are rapidly gaining prominence as a measure of complex sound processing in the brainstem and midbrain. In spite of numerous studies reporting changes in hearing thresholds, ABR wave amplitudes, and the FFRs and EFRs under neurodegenerative conditions, including aging, the relationships between these metrics are not clearly understood. In this study, the relationships between ABR thresholds, ABR wave amplitudes, and EFRs are explored in a rodent model of aging. ABRs to broadband click stimuli and EFRs to sinusoidally amplitude-modulated noise carriers were measured in young (3-6 months) and aged (22-25 months) Fischer-344 rats. ABR thresholds and amplitudes of the different waves as well as phase-locking amplitudes of EFRs were calculated. Age-related differences were observed in all these measures, primarily as increases in ABR thresholds and decreases in ABR wave amplitudes and EFR phase-locking capacity. There were no observed correlations between the ABR thresholds and the ABR wave amplitudes. Significant correlations between the EFR amplitudes and ABR wave amplitudes were observed across a range of modulation frequencies in the young. However, no such significant correlations were found in the aged. The aged click ABR amplitudes were found to be lower than would be predicted using a linear regression model of the young, suggesting altered gain mechanisms in the relationship between ABRs and FFRs with age. These results suggest that ABR thresholds, ABR wave amplitudes, and EFRs measure complementary aspects of overlapping neurophysiological processes and the relationships between these measurements changes asymmetrically with age. Hence, measuring all three metrics provides a more complete assessment of auditory function, especially under pathological conditions like aging.