  In this paper we study the commutators of fractional type integral operators.
This operators are given by kernels of theform
$$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles
matrices and each $k_i$ satisfies a fractional size condition and generalized
fractional H\"ormander condition. We obtain weighted Coifman estimates,
weighted $L^p(w^p)$ - $L^q(w^q)$ estimates and weighted BMO estimates. We also
give a two weight strong estimate for pair of weights of the form $(u,Su)$
where $u$ is an arbitrary non-negative function and $S$ is a maximal operator
depending on the smoothness of the kernel $K$. For the singular case we also
give a two-weighted endpoint estimate.
