The effects of aging and age-related hearing loss on the ability to learn degraded speech are not well understood. This study was designed to compare the perceptual learning of time-compressed speech and its generalization to natural-fast speech across young adults with normal hearing, older adults with normal hearing, and older adults with age-related hearing loss. Early learning (following brief exposure to time-compressed speech) and later learning (following further training) were compared across groups. Age and age-related hearing loss were both associated with declines in early learning. Although the two groups of older adults improved during the training session, when compared to untrained control groups (matched for age and hearing), learning was weaker in older than in young adults. Especially, the transfer of learning to untrained time-compressed sentences was reduced in both groups of older adults. Transfer of learning to natural-fast speech occurred regardless of age and hearing, but it was limited to sentences encountered during training. Findings are discussed within the framework of dynamic models of speech perception and learning. Based on this framework, we tentatively suggest that age-related declines in learning may stem from age differences in the use of high- and low-level speech cues. These age differences result in weaker early learning in older adults, which may further contribute to the difficulty to perceive speech in daily conversational settings in this population.