Suppose (R,m) →(S,n) is a local homomorphism of lo­cal rings. We show that if M is a Matlis reflexive R-module, then _R(S,M) and Tor^R(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 if M is a reflexive R-module, then [Rcirc] ⊗_R M is a reflexive [Rcirc]-module and in fact We also show that if R is any local ring and M and N are two reflexive Ä-modules, then Ext_R(M,N) and Tor^R(M,N) are reflexive R-modules for all i.