In this paper, we give some pointwise convergence and Fatou type convergence theorems for a family of nonlinear bivariate singular integral operators in the following form: urn:x-wiley:mma:media:mma5425:mma5425-math-0006 where m1,m2 ≥ 1 are fixed natural numbers, and ω ∈ Ω, Ω denotes a nonempty set of indices endowed with a topology. Here, denotes a family of kernel functions and f belongs to the space of Lebesgue integrable functions . Some numerical examples and graphical illustrations supporting the results are also given.