  We classify all compact simply connected homogeneous CR manifolds $M$ of
codimension one and with non-degenerate Levi form up to CR equivalence. The
classification is based on our previous results and on a description of the
maximal connected compact group $G(M)$ of automorphisms of $M$. We characterize
also the standard homogeneous CR manifolds as the homogeneous CR manifolds
whose group $G(M)$ in not semisimple.
