The definition of a reductive Lie group used by many authors is that of a finite covering of a linear reductive Lie group. This definition excludes simply connected hermitian Lie groups and the point of this talk is to argue that the methods used to prove the asymptotic expansion of matrix coefficients, the Casselman Subrepresentation Theorem, the Automatic Continuity Theorem for n-finite functionals and the Krötz-Stanton Extension Theorem generalize to these groups as well.