  The excitation by a high frequency field of multi--level quantum systems with
a slowly varying density of states is investigated. A general approach to study
such systems is presented. The Floquet eigenstates are characterized on several
energy scales. On a small scale, sharp universal quasi--resonances are found,
whose shape is independent of the field parameters and the details of the
system. On a larger scale an effective tight--binding equation is constructed
for the amplitudes of these quasi--resonances. This equation is non--universal;
two classes of examples are discussed in detail.
