  We prove that if two real-analytic hypersurfaces in $\mathbb C^2$ are
equivalent formally, then they are also $C^\infty$ CR-equivalent at the
respective point. As a corollary, we prove that all formal equivalences between
real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (in
particular are convergent). The result is obtained by using the recent {\em CR
- DS technique}, connecting degenerate CR-manifolds and Dynamical Systems, and
employing subsequently the {\em multisummability theory} of divergent power
series used in the Dynamical Systems theory.
