  We consider a medium of multilevel atomic systems interacting with radiation
pulses. A relatively simple technique of analytic calculations is proposed,
which allows revealing all necessary conditions (with sufficient conditions to
be checked separately) imposed on the interaction parameters, for which the
mean dipole moment of a multilevel atomic medium vanishes, i.e., the medium
becomes transparent via adiabatic interaction. The proposed technique is based
on the method of quasienergies and illustrated for three- and five-level atomic
systems. The necessary conditions for the propagation length where the
interaction adiabaticity is preserved in the medium are obtained.
