On the Continuity of the Eigenvalues of a Sublaplacian We study the behavior of the eigenvalues of a sublaplacian $\Delta_b$ on a compact strictly pseudoconvex CR manifold $M$, as functions on the set ${\mathcal P}_+$ of positively oriented contact forms on $M$ by endowing ${\mathcal P}_+$ with a natural metric topology. Keywords:CR manifold, contact form, sublaplacian, Fefferman metricCategories:32V20, 53C56