  In this paper, we show the strong and weak type boundedness of
$T_{\Omega,\alpha}^A$ and $M_{\Omega,\alpha}^A$, the multilinear fractional
integral operators and the corresponding fractional maximal operators, on the
two weights weighted Morrey space. Furthermore, we also obtain the mulitilinear
singular integral operators $T_{\Omega}^A$ and the corresponding maximal
operators $M_{\Omega}^A$ are strong bounded operators on the same spaces.
