  Sequences of bivariate orthogonal polynomials written as vector polynomials
of increasing size satisfy a couple of three term relations with matrix
coefficients. In this work, introducing a time-dependent parameter, we analyse
a Lax-type pair system for the coefficients of the three term relations. We
also deduce several characterizations relating the Lax-type pair, the shape of
the weight, Stieltjes function, moments, a differential equation for the
weight, and the bidimensional Toda-type systems.
