  We investigate CR-manifolds which are tubes M:= F x iV over general bases F
in a real vector space V and characterize the k-nondegeneracy of M in terms of
the real affine geometry of F. We give a method for an explicit computation of
the Lie algebra hol(M,a) of all local infinitesimal CR-transformations at a and
use these local invariants to establish the CR-inequivalence of certain
families of CR-manifolds. In dimension 5 we present, apart from the well known
tube over the future light cone, new examples of 2-nondegenerate homogeneous
CR-manifolds that are mutually locally CR-inequivalent.
