This paper is in continuation of our work in [24], wherein we studied someapproximation properties of the Stancu-Durrmeyer operators based on q-integers. Here,we construct a bivariate generalization of these operators and study the rate of convergenceby means of the complete modulus of continuity and the partial moduli of continuity andthe degree of approximation with the aid of the Peetre's K functional. Subsequently, wedene the GBS(Generalized Boolean Sum) operators of Stancu- Durrmeyer type and givethe rate of approximation by means of the mixed modulus of smoothness and the Lipschitzclass of Bogel-continuous functions.