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In this contribution we present the results of a study on land mobile satellite channel models for satellite systems with multiple satellites. The slow fading of our channel model for several satellites is based on a Markov channel state model for joint processes while the probability density function (PDF) of the signal amplitude within each state is fitted to the Loo distribution. The correlation between two satellite channels and the channel spatial autocorrelation have also been studied. We show that a channel state model that uses a Markov state model of order one or of a fixed higher order is not appropriate if the state duration is of very high importance, which can be the case in the process of system planning. Therefore, we propose a dynamic higher order Markov state model for joint processes that depends on the current state duration. This approach models precisely any PDF of the channel state duration for both single and multiple satellite broadcasting systems while having a significantly lower computational complexity than a fixed higher order Markov model. It models the channel states of the whole system correctly, as well as the channel states of each satellite observed independently. It is able to capture the state correlation between multiple satellites. We also study possible approximations of the proposed models in order to reduce their computational complexity while having a good PDF match. Our channel state models are validated by measurements.