Suppose (R,m) →(S,n) is a local homomorphism of lo­cal rings. We show that if M is a Matlis reflexive R-module, thenR(S,M) and TorR(S,M) are Matlis reflexive S-modules if S is module-finite over the image of R. In case S = [Rcirc], the m-adic comple­tion of A, we show that ifMis a reflexive R-module, then [Rcirc] ⊗RMis a reflexive [Rcirc]-module and in factWe also show that if R is any local ring andMandNare two reflexive Ä-modules, then ExtR(M,N) and TorR(M,N) are reflexiveR-modules for all i.