  Hypersurface type CR-structures with non-degenerate Levi form on a manifold
of dimension $(2n+1)$ have maximal symmetry dimension $n^2+4n+3$. We prove that
the next (submaximal) possible dimension for a (local) symmetry algebra is
$n^2+4$ for Levi-indefinite structures and $n^2+3$ for Levi-definite structures
when $n>1$. In the exceptional case of CR-dimension $n=1$, the submaximal
symmetry dimension 3 was computed by E.\,Cartan.
