Auditory tasks such as understanding speech and making music rely on our ability to track those sounds and adjust our attention based on the temporal cues they contain. An entrainment approach proposes that internal oscillatory mechanisms underlie these abilities by synchronizing to rhythms in the external world. Here, we aimed to understand the factors that facilitate and impede rhythm processing by investigating the interplay between properties of external and internal rhythms. We focused on two key properties of an oscillator: its preferred rate, the default rate at which it oscillates in the absence of input; and flexibility, its ability to adapt to changes in rhythmic context. We hypothesized that flexibility would be diminished with advancing age. Experiment 1 was a two-session duration discrimination paradigm where we developed methods to estimate preferred rate and flexibility and assessed their reliability. Experiment 2 involved a shorter version of this paradigm and a paced tapping task with matched stimulus conditions, in addition to a spontaneous motor tempo (SMT), and two preferred perceptual tempo (PPT) tasks that measured motor and perceptual rate preferences, respectively. Preferred rates, estimated as the stimulus rates with best performance for each individual were showed harmonic relationship across sessions (Experiment 1), and were correlated with SMT (Experiment 2). Interestingly, estimates from motor tasks were slower than those from the perceptual task, and the degree of slowing was consistent for each individual. In order to challenge individuals’ flexibility, we maximized the differences in stimulus rates between consecutive trials in the duration discrimination and paced tapping tasks. As a result, performance in both tasks decreased, and performance on individual trials indicated a gravitation towards the stimulus rate presented on the preceding trial. Critically, flexibility, quantified as individuals’ ability to adapt to faster-than-previous rates, decreased with age. Overall, the findings support that an oscillatory system with domain-specific rate preferences underlies perception and production of rhythms, and that this system loses its ability to flexibly adapt to changes in the external rhythmic context in ageing.