Compact homogeneous CR manifolds

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.