We introduce a new method for approximate inference in Hybrid Dynamical Graphical models, in particular, for switching dynamical networks. For the important special case of switching linear Gaussian state space models (switching Kalman Filters), our method is a novel form of Gaussian sum smoother, consisting of a single forward and backward pass. Our method is particularly well suited to switching observation models, since one of the key approximations is obviated. We compare our method very favourably against a range of competing techniques, including sequential Monte Carlo and Expectation Propagation, for which we also derive a novel numerically more stable implementation using the `auxiliary variable trick'. We show that the use of mixture representations for both filtering and smoothing can dramatically improve the quality of the approximation .