  We introduce new invariant tensors in CR structures which can be viewed as
higher order Levi forms. Using the second and third order tensors, we give a
complete formal normal form (in the sense of Chern-Moser) for a real
hypersurface at a generic Levi degeneracy. (We say that M has a generic Levi
degeneracy at p if the Levi determinant vanishes at p but its differential does
not, and the set of Levi degenerate points of M is transverse to the Levi null
space at p.) By applying a convergence theorem for formal mappings due to the
author, Baouendi, and Rothschild, we conclude that the above mentioned formal
normal form provides a complete set of biholomorphic invariants for
real-analytic hypersurfaces at generic Levi degeneracies.
