  We illustrate a completely analytic approach to Mel'nikov theory, which is
based on a suitable extension of a classical method, and which is parallel and
-- at least in part -- complementary to the standard procedure. This approach
can be also applied to some ``degenerate'' situations, as to the case of
nonhyperbolic unstable points, or of critical points located at the infinity
(thus giving rise to unbounded orbits, e.g. the Keplerian parabolic orbits),
and it is naturally ``compatible'' with the presence of general symmetry
properties of the problem.
