Detection of frequency modulation (FM) with rate = 10 Hz may depend on conversion of FM to amplitude modulation (AM) in the cochlea, while detection of 2-Hz FM may depend on the use of temporal fine structure (TFS) information. TFS processing may worsen with greater age and hearing loss while AM processing probably does not. A two-stage experiment was conducted to test these ideas while controlling for the effects of detection efficiency. Stage 1 measured psychometric functions for the detection of AM alone and FM alone imposed on a 1-kHz carrier, using 2- and 10-Hz rates. Stage 2 assessed the discrimination of AM from FM at the same modulation rate when the detectability of the AM alone and FM alone was equated. Discrimination was better for the 2-Hz than for the 10-Hz rate for all young normal-hearing subjects and for some older subjects with normal hearing at 1 kHz. Other older subjects with normal hearing showed no clear difference in AM-FM discrimination for the 2- and 10-Hz rates, as was the case for most older hearing-impaired subjects. The results suggest that the ability to use TFS cues is reduced for some older people and most hearing-impaired people.