  We establish inequalities for the eigenvalues of the sub-Laplace operator
associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR
manifold. Our inequalities extend those obtained by Niu and Zhang
\cite{NiuZhang} for the Dirichlet eigenvalues of the sub-Laplacian on a bounded
domain in the Heisenberg group and are in the spirit of the well known
Payne-P\'{o}lya-Weinberger and Yang universal inequalities.
