The problem considered in this paper is the problem of the exact calculation of smoothing in hidden switching state-space systems. There is a hidden state-space chain X, the switching Markov chain R, and the observed chain Y. In the classical, widely used “conditionally Gaussian state-space linear model” (CGSSLM) the exact calculation with complexity linear in time is not feasible and different approximations have to be made. Different alternative models, in which the exact calculations are feasible, have been re-cently proposed (2008). The core difference between these models and the classical ones is that the couple (R, Y) is a Markov one in the recent models, while it is not in the clas-sical ones. Here we propose a further extension of these recent models by relaxing the hypothesis of the Markovianity of X conditionally on (R, Y). In fact, in all classical mod-els and as well as in the recent ones, the hidden chain X is always a Markov one condi-tionally on (R, Y). In the proposed model it can be of any form. In particular, different “long memory” processes can be considered. In spite of this larger generality, we show that the smoothing formulae are still calculable exactly with the complexity polynomial in time