Let \((p_n)_{n\geq 0}\) be a monic orthogonal polynomial sequence with respect to a positive weight function \(\rho(x)\) supported on the interval \((a,b)\in\mathbb R\). It is well known that \(p_n\) satisfy a three-term recurrence relation \[ p_{n+1}(x)=(x-a_n)p_{n-1}(x)-b_n p_n(x), \] with the condition \(p_0(x)=1\) and \(p_1(x)=x-a_1\). The associated polynomials \(p_n^{(1)}(x)\) satisfy the same three-term recurrence relation but with the initial conditions \(p_0^{(1)}(x)=0\) and \(p_1^{(1)}(x)=b_1\). Then the Stieltjes Theorem (also known as Markov Theorem) states that \[ \lim_{n\to\infty}\frac{p_n^{(1)}(x)}{p_n(x)}= \int_a^b \frac{\rho(x)}{x-z}dz, \] and the convergence is uniform in \(\mathbb C\setminus{(a,b)}\). In the present paper the authors consider the case of orthogonal polynomials in two variables. In this case the standard techniques fail and the result is not given in terms of the orthogonal polynomials theirselves and involve some invariant factor for orthogonal polynomials.