Abstract: Let A and B be unital Banach algebras, and let M be a Banach A, B-bimodule. Then T=(^{A M}_B) becomes a triangular Banach algebra when equipped with the usual matrix operation and a Banach space norm ‖(^{a m}_b)‖=‖a‖_A+‖m‖_M+‖b‖_B. T^*=(^{A* M*}_B^*) is the dual space of T by the action (^{f h}_g)(^{a m}_b)=f(a)+h(m)+g(b). T^* becomes a dual Banach T- bimodule with the module action defined by am (^{a m}_b)·(^{f h}_g)=(^{a·f+m·h b·h}_b·g), (^{f h}_g)·(^{a m}_b)=(^{f·a h·a}_h·m+g·b). The map from T into T^* is called dual module map. We investigate the dual module Jordan derivations and dual module generalized derivations on T, giving a condition under which a dual module Jordan derivation is a dual module derivation and a characterization of dual module generalized derivation.

Key words: triangular Banach algebra, dual Banach bimodule, dual module generalized derivation, dual module Jordan derivation