  This article studies the fundamental invariants of 2--nondegenerate CR
geometries with simple models. We show that there are two sources of these
invariants. The first source is the harmonic curvature of the parabolic
geometry that appears (locally) on the leaf space of the Levi kernel. The
second source is the difference between the complex structure on the complex
tangent space of the CR geometry and the complex structure on the
correspondence space to the underlying parabolic geometry. We show that the
later fundamental invariants appear only when the model is generic and if they
vanish, then the solution of the local equivalence problem of 2--nondegenerate
CR geometries with simple models is provided by the Cartan connection of the
underlying parabolic geometry. We show that nontrivial examples of CR
geometries with the later fundamental invariants can be obtained as
deformations of the models.
