Normal-hearing older adults often experience increased difficulties understanding speech in noise. In addition, they benefit less from amplitude fluctuations in the masker. These difficulties may be attributed to an age-related auditory temporal processing deficit. However, a decline in cognitive processing likely also plays an important role. This study examined the relative contribution of declines in both auditory and cognitive processing to the speech in noise performance in older adults. Participants included older (60–72 years) and younger (19–29 years) adults with normal hearing. Speech reception thresholds (SRTs) were measured for sentences in steady-state speech-shaped noise (SS), 10-Hz sinusoidally amplitude-modulated speech-shaped noise (AM), and two-talker babble. In addition, auditory temporal processing abilities were assessed by measuring thresholds for gap, amplitude-modulation, and frequency-modulation detection. Measures of processing speed, attention, working memory, Text Reception Threshold (a visual analog of the SRT), and reading ability were also obtained. Of primary interest was the extent to which the various measures correlate with listeners’ abilities to perceive speech in noise. SRTs were significantly worse for older adults in the presence of two-talker babble but not SS and AM noise. In addition, older adults showed some cognitive processing declines (working memory and processing speed) although no declines in auditory temporal processing. However, working memory and processing speed did not correlate significantly with SRTs in babble. Despite declines in cognitive processing, normal-hearing older adults do not necessarily have problems understanding speech in noise as SRTs in SS and AM noise did not differ significantly between the two groups. Moreover, while older adults had higher SRTs in two-talker babble, this could not be explained by age-related cognitive declines in working memory or processing speed.