The goal of the talk is to discuss some recent results
joint work with Bernhard Lamel) concerning the structure of the
global groups of CR automorphisms of real-analytic CR manifolds,
levi-form is allowed to degenerate. We will mainly focus on the
real-analytic hypersurfaces containing no holomorphic curves and
show that in
such a setting the local automorphism groups can be analytically
by a finite jet at any given point.