  We give an explicit verifiable characterization of weakly pseudoconvex but
locally nonconvexifiable hypersurfaces of finite type in dimension two. It is
expressed in terms of a generalized model, which captures local geometry of the
hypersurface both in the complex tangential and nontangential directions. As an
application we obtain a new class of nonconvexifiable pseudoconvex
hypersurfaces with convex models.
