Abstract: It is well-known that a real-analytic function on the real line is a restriction of a holomorphic (analytic) function. In several complex variables there are more kinds of submanifolds than just real curves. Severi's theorem says that a real-analytic CR function on a real-analytic CR submanifold is a restriction of a holomorphic function. So the Cauchy-Riemann equations restricted to the manifold are enough. We extend this result to some CR singular submanifolds, that is when the Cauchy-Riemann equations induce a problem with a characteristic point. It is joint work with Alan Noell and Sivaguru Ravisankar.