\input zb-basic \input zb-ioport \iteman{io-port 00140589} \itemau{Flandoli, Franco} \itemti{Stochastic evolution equations with non-coercive monotone operators.} \itemso{Stochastic partial differential equations and their applications, Proc. IFIP Int. Conf., Charlotte/NC (USA) 1991, Lect. Notes Control Inf. Sci. 176, 70-80 (1992).} \itemab [For the entire collection see Zbl 0754.00020.] This paper is devoted to the detailed study of a particular stochastic evolution equation with non-coercive monotone operators. The Schr\"odinger and wave equations are shown to satisfy the theory developed here. \itemrv{A.Dale (Durban)} \itemcc{} \itemut{stochastic evolution equation; Schr\"odinger and wave equations} \itemli{} \end