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The focus of this work is on robot learning of cyclic motions. The term `cyclic' refers to motions which are repeated, but do not have a strictly defined period. The dynamics of a set of human demonstrated cyclic motions is approximated with mixtures of linear systems. The particular problems that are tackled here are: the inconsistency in periodicity of cyclic motions, occurrence of high accelerations in the transient period when reproducing the learned dynamics, and learning trajectories that involve a combination of translatory and cyclic motion components. Solutions are proposed for the aforementioned problems, and their validity is assessed through simulations. The proposed work can find implementation in learning from observation of cyclic industrial tasks (e.g., painting, peening) or service tasks (e.g., ironing, wiping).