Learning motion patterns in dynamic environments is a key component of any context-aware robotic system, and probabilistic mixture models provide a sound framework for mining these patterns. This paper presents an approach for learning motion models from trajectories provided by the tracking system of a moving platform. We present a learning approach in which a Linear Dynamical System (LDS) is augmented with a discrete hidden variable that has a number of states equal to the number of behaviours in the environment. As a result, a mixture of linear dynamical systems (MLDSs) capable of explaining several motion behaviours is developed. The model is learned by means of the Expectation Maximization (EM) algorithm.