Learning dynamical systems is one of the important problems in many fields. In this paper, we present an algorithm for learning non-linear dynamical systems which works by aligning local linear models, based on a probabilistic formulation of subspace identification. Because the procedure for constructing a state sequence in subspace identification can be interpreted as the CCA between past and future observation sequences, we can derive a latent variable representation for this problem. Therefore, as in a similar manner to the recent works on learning a mixture of probabilistic models, we obtain a framework for constructing a state space by aligning local linear coordinates. This leads to a prominent algorithm for learning non-linear dynamical systems. Finally, we apply our method to motion capture data and show how our algorithm works well. © 2010 IEEE.