Аннотация:The paper introduces a set of Hidden Markov Models (HMM), driven by a special class of Markov jump processes [2] and [3]. The Markovian property for the couple "jump process-governed diffusion" is proved. A system of corresponding integro-differential Fokker-Plank type equations for the transition probability is derived. Analysis and special cases of this system such as the classic HMM and systems with one jump are also considered.