Abstract Recent years have seen the development of efficient and provably correct spectral algorithms for learning models of partially observable environments arising in many applications. But despite the high hopes raised by this new class of algorithms, their practical impact is still below expectations. One reason for this is the difficulty in adapting spectral methods to exploit structural constraints about different target environments which can be known beforehand. A natural structure intrinsic to many dynamical systems is a multi-resolution behaviour where interesting phenomena occur at different time scales during the evolution of the system. In this paper we introduce the multi-step predictive state representation (M-PSR) and an associated learning algorithm that finds and leverages frequent patterns of observations at multiple scales in dynamical systems with discrete observations. We perform experiments on robot exploration tasks in a wide variety of environments and conclude that the use of M-PSRs improves over the classical PSR for varying amounts of data, environment sizes, and number of observations symbols.