It is well known that some (one dimensional) Markov processes are related with orthogonal polynomials.
Such are the cases of random walks and birth and death processes, if the state space S is taken to be
discrete, and diusion processes, where the state space S is a real interval. In this talk we will explain with
some examples how the matrix orthogonality plays an important role in order to give an interpretation of
bivariate Markov processes, i.e. Markov processes assuming values in Sf1;2; : : : ;Ng, where S  R and N
is a nonnegative integer. We will focus in the case where both components are dependent and give some
examples where S is discrete or continuous.