A new approach is introduced in this paper for dynamic modeling and dimensionality reduction from time series of curves. For this purpose, a dynamic mixture of experts model whose regression coefficients evolve from curve to curve according to a Gaussian random walk over low dimensional factors, is proposed. The resulting model is neither else than a particular state-space model involving discrete and continuous latent variables, whose parameters are learned across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated sequences of curves has shown the strong potential of the proposed approach.