There is a large amount of variability in performance in masked-speech reception tasks, as well as in psychophysical auditory temporal processing tasks, between listeners with normal or relatively normal low-frequency hearing. In this study we used a cross-sectional dataset collected on 102 listeners (34 young, 34 middle-aged, 34 older) to assess whether variance in these tasks could be explained by variance in subcortical electrophysiological measures of auditory function (auditory brainstem responses and frequency following responses), and whether variance in speech-reception performance could be explained by variance in auditory temporal processing tasks. The potential confounding effect of high-frequency sensitivity was strictly controlled for by using highpass masking noise. Because each high-level construct (masked-speech reception, auditory temporal processing, and subcortical electrophysiological function) was indexed by several variables, we used principal component analyses to reduce the dimensionality of the dataset. Multiple-regression models were then used to assess the associations between the extracted principal components while controlling for a range of possible confounders including age and audiometric thresholds. We found that masked-speech reception was credibly associated with psychophysical auditory temporal processing abilities. No credible associations were found between masked-speech reception and electrophysiological measures of subcortical auditory function, or between psychophysical measures of auditory temporal processing and electrophysiological measures of subcortical auditory function. These results suggest that either the electrophysiological measures of subcortical auditory function used were not sufficiently sensitive to the subcortical neural processes limiting performance in the speech-reception and psychophysical auditory temporal-processing tasks, or that variance in these tasks is largely unrelated to variance in subcortical neural processes in listeners with near-normal hearing.