Invariants of elliptic and hyperbolic CR-structures of codimension 2

We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-c odimension 2 to parallelisms thus serving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequ ence of two principal bundles over the manifold, takes values in the Lie al gebra of infinitesimal automorphisms of the quadric corresponding to the Le vi form of the manifold, and behaves "almost" like a Cartan connection. The construction is explicit and allows us to study the properties of the para llelism as well as those of its curvature form. It also leads to a natural class of "semi-flat" manifolds for which the two bundles reduce to a single one and the parallelism turns into a true Cartan connection. In addition, for rear-analytic manifolds we describe certain local normal f orms that do not require passing to bundles, but in many ways agree with th e structure of the parallelism.