Hidden Markov models have been extended in many directions, leading to pairwise Markov models, triplet Markov models, or discriminative random fields, all of which have been successfully applied in many fields covering signal and image processing. The Dempster-Shafer theory of evidence has also shown its interest in a wide range of situations involving reasoning under uncertainty and/or information fusion. There are, however, only few works dealing with both of these modeling tools simultaneously. The aim of this paper, which falls under this category of works, is to propose a general evidential Markov model offering wide modeling and processing possibilities regarding information imprecision, sensor unreliability and data fusion. The main interest of the proposed model relies in the possibility of achieving, easily, the Dempster-Shafer fusion without destroying the Markovianity