In this paper some approximation formulae for a class of convolution typedouble singular integral operators depending on three parameters of the type$$( T_{\lambda }f) ( x,y)=\int_{a}^{b}\int_{a}^{b}f(t,s) K_{\lambda}(t-x,s-y) dsdt, \quad x,y\in (a,b), \quad \lambda \in \Lambda \subset[ 0,\infty ), $$are given. Here *f* belongs to the function space $L_{1}( \langlea,b\rangle ^{2}),$ where $\langle a,b\rangle $ isan arbitrary interval in $\mathbb{R}$. In this paper three theorems areproved, one for existence of the operator $( T_{\lambda }f)( x,y) $ and the others for its Fatou-type pointwise convergenceto $f(x_{0},y_{0}),$ as $(x,y,\lambda )$ tends to $(x_{0},y_{0},\lambda_{0}).$ In contrast to previous works, the kernel functions $K_{\lambda}(u,v)$ don't have to be $2\pi$-periodic, positive, even and radial. Ourresults improve and extend some of the previous results of [1,6,8,10,11,13] in three dimensional frame andespecially the very recent paper [15].