We introduce and study property T and strong property T for unital *-homomorphisms between two unital C*-algebras.We also consider the relations between property T and invariant subspaces for some canonical unital *-representations.As a corollary,we show that when G is a discrete group,G is finite if and only if G is amenable and the inclusion map i: C*r(G) → B(l2(G))has property T.We also give some new equivalent forms of property T for countable discrete groups and strong property T for unital C*-algebras.