In this work, we discuss the L p boundedness of several classes of integral operators with homogeneous kernels on product domains. We establish L p boundedness of singular and Marcinkiewicz integral operators on product domains when their kernels are in L(log L)2(Sn−1 × Sm−1). We also proved the Lp boundedness of Marcinkiewicz integral operators on product domains provided that the kernels satisfy Grafakos-Stevanov’s size conditions. Furthermore, we study the L p boundedness of a class of singular integral operators along twisted surfaces with kernels belonging to the space L(log L) 2 (S n−1 × S m−1 ). Finally, we prove some weighted norm inequality of a class of Marcinkiewicz integral operators on product domains along various surfaces provided that the kernels are in L(log L) 2 (S n−1 × S m−1 ).