  The concept of quasiresonance was introduced in connection with inelastic
collisions between one atom and a vibro-rotationally excited diatomic molecule.
In its original form, the collisions induce {\sl quasiresonant} transfer of
energy between the internal degrees of freedom of the diatom: there is a
surprisingly accurate low order rational value for the ratio of the changes in
the vibrational and rotational classical actions, provided the vibrational and
rotational frequencies of the diatom are approximately related by low order
rational values, and the collision was longer that the rotational period of the
molecule. In this paper we show that quasiresonance can be extended to many
other processes and systems, and that it may be understood in terms of the
adiabatic invariance theory and the method of averaging.
