Listeners vary in the perception and interpretation of speech prosody (the variations in intonation, loudness, and rhythm of spoken language). The source of this variability is unknown. We investigated whether the ability to recognise and classify prosodic structure is related to working memory (WM) capacity. This hypothesis stems from the tight connection between prosodic and syntactic (grammatical) structure, while processing syntax is known to relate to WN capacity. Healthy adult speakers of Dutch judged prosodic structures in a gating paradigm. The phrases contained early and late intonational cues that signalled whether the phrases contained an internal grouping or not. Listeners also took part in WM (digit span) and processing speed (letter comparison) tasks. There was an interaction between performance in the prosody judgement and WM tasks: high-WM listeners were better at classifying prosodic structure and required less prosodic information to detect the correct structure. There was no interaction between prosody processing and processing speed, suggesting that the interaction between prosodic judgement and WM capacity was not due to motivational or attentional differences. The results demonstrate a close relationship between prosody processing and WM abilities, implying that WM is an important component of prosody processing.