  A comparative discussion of the normal form and action angle variable method
is presented in a tutorial way. Normal forms are introduced by Lie series which
avoid mixed variable canonical transformations. The main interest is focused on
establishing a third integral of motion for the transformed Hamiltonian
truncated at finite order of the perturbation parameter. In particular, for the
case of the action angle variable scheme, the proper canonical transformations
are worked out which reveal the third integral in consistency with the normal
form. Details are discussed exemplarily for the Henon-Heiles Hamiltonian. The
main conclusions are generalized to the case of n perturbed harmonic
oscillators.
