In 2013, Ren and Zeng de�ned the genuine q-Bernstein-Schurer operators and investigated the statistical approximation properties of these operators. In the present paper, we introduce the (p; q)-analogue of these q-operators and establish a Korovkin type approximation theorem and estimate the rate of convergence of these (p; q) operators by means of Lipschitz class function and the Peetre's ... [Show full abstract] K-functional. Subsequently, we de�ne the bivariate case of the genuine (p; q)-Bernstein-Schurer operators and study some approximation theorems of these operators with the help of partial moduli of continuity, complete modulus of continuity and Peetre's K-functional. Lastly, we consider the associated GBS operators of the Bernstein-Schurer type and study some of its approximation properties for Bogel continuous and Bogel di�erentiable functions. Furthermore, we show the rate of convergence of the above operators to certain functions by illustrative graphics using Maple algorithms.