Motion imitation requires reproduction of a dynamical signature of a movement, i.e. a robot should be able to encode and reproduce a particular path together with a specific velocity and/or an acceleration profile. Furthermore, a human provides only few demonstrations, that cannot cover all possible contexts in which the robot will need to reproduce the motion autonomously. Therefore, the encoding should be able to efficiently generalize knowledge by generating similar motions in unseen context. This work follows a recent trend in Programming by Demonstration in which the dynamics of the motion is learned. We present an algorithm to estimate multivariate robot motions through a Mixture of Gaussians. The strengths of the proposed encoding are three-fold: i) it allows to generalize a motion to unseen context; ii) it provides fast on-line replanning of the motion in the face of spatio-temporal perturbations; iii) it may embed different types of dynamics, governed by different attractors. The generality of the method to estimate arbitrary nonlinear motion dynamics is demonstrated by accurately estimating a set of known non-linear dynamical systems. The platformindependency and real-time performance of the method are further validated to learn the non-linear motion dynamics of manipulation tasks with different robotic platforms. We provide an experimental comparison of our approach with an related state-of-the-art method.