  In this paper the class of mixed renewal processes (MRPs for short) with
mixing parameter a random vector from \cite{lm6z3} (enlarging Huang's \cite{hu}
original class) is replaced by the strictly more comprising class of all
extended MRPs by adding a second mixing parameter. We prove under a mild
assumption, that within this larger class the basic problem, whether every
Markov process is a mixed Poisson process with a random variable as mixing
parameter has a solution to the positive. This implies the equivalence of
Markov processes, mixed Poisson processes, and processes with the multinomial
property within this class. In concrete examples we demonstrate how to
establish the Markov property by our results. Another consequence is the
invariance of the Markov property under certain changes of measures.
