In this paper, we study one kind of Markov Skeleton processes, nonhomogeneous (H,Q) processes, and we mainly focus on their distributions and moments of the first entrance time. With detailed analysis, we obtain their recursive formula and some related properties. And as one kind of nonhomogeneous (H;Q) processes, Nonhomogeneous Semi-Markov Process, we study it’s distributions and moments of the first entrance time, and we also obtain their recursive formula.