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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   2K  λ    (  t  −  x  ,  s  −  y  ,  f  (  t  ,  s  )  )  d  s  d  t  ,    (  x  ,  y  )  ∈R   2    ,  λ  ∈  Λ  ,    $${T_\lambda }(f;x,y) = \iint\limits_{{\mathbb{R}^2}}K_\lambda {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb{R}^2},\lambda  \in \Lambda ,}$$    where Λ is a set of non-negative numbers with accumulation point λ0.

A new approach to nonlinear singular integral operators depending on three parameters