We define analytic $R$-groups for affine Hecke algebras, and prove the analog
of the Knapp-Stein Dimension Theorem. As a corollary we prove that the
commutant algebra of a unitary principal series representation is isomorphic to
the complex group algebra of the $R$-group, twisted by a certain 2-cocycle
$\gamma$. For classical Hecke algebras we prove that $\gamma$ is always
trivial.