It has been shown that certain resonance relations determine the stability type of the approximate generalized symmetries. The normal forms have been shown to be the unstable approximate generalized symmetries. An approximate version of the Noether's theorem has been given for the Hamiltonian systems. Furthermore, a comparison of KAM curves obtained analytically from an approximate first integral with those computed numerically has been given for a two dimensional galaxy model. (C) 2000 Elsevier Science B.V. All rights reserved. AMS classification: 58F35: 58A10: 70H10.