1. Hidden Markov models are prevalent in animal movement modelling, where they are widely used to infer behavioural modes and their drivers from various types of telemetry data. To allow for meaningful inference, observations need to be equally spaced in time, or otherwise regularly sampled, where the corresponding temporal resolution strongly affects what kind of behaviours can be inferred from the data. 2. Recent advances in biologging technology have led to a variety of novel telemetry sensors which often collect data from the same individual simultaneously at different time scales, e.g. step lengths obtained from GPS tags every hour, dive depths obtained from time-depth recorders once per dive, or accelerations obtained from accelerometers several times per second. However, to date, statistical machinery to address the corresponding complex multi-stream and multi-scale data is lacking. 3. We propose hierarchical hidden Markov models as a versatile statistical framework that naturally accounts for differing temporal resolutions across multiple variables. In these models, the observations are regarded as stemming from multiple, connected behavioural processes, each of which operates at the time scale at which the corresponding variables were observed. 4. By jointly modelling multiple data streams, collected at different temporal resolutions, corresponding models can be used to infer behavioural modes at multiple time scales, and in particular help to draw a much more comprehensive picture of an animal's movement patterns, e.g. with regard to long-term vs. short-term movement strategies. 5. The suggested approach is illustrated in two real-data applications, where we jointly model i) coarse-scale horizontal and fine-scale vertical Atlantic cod (Gadus morhua) movements throughout the English Channel, and ii) coarse-scale horizontal movements and corresponding fine-scale accelerations of a horn shark (Heterodontus francisci) tagged off the Californian coast.