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In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , $$T_{\lambda }(f;x,y)=\underset{{ℝ}^2}{\int \int }(t-x,s-y,f(t,s))dsdt,(x,y)\in {ℝ}^2,\lambda \in \Lambda ,$$ where Λ is a set of non-negative numbers with accumulation point λ0.