  We study linear problems of mathematical physics in which the adiabatic
approximation is used in the wide sense. Using the idea that all these problems
can be treated as problems with operator-valued symbol, we propose a general
regular scheme of adiabatic approximation based on operator methods. This
scheme is a generalization of the Born-Oppenheimer and Maslov methods, the
Peierls substitution, etc. The approach proposed in this paper allows one to
obtain "effective" reduced equations for a wide class of states inside terms
(i.e., inside modes, subregions of dimensional quantization, etc.) with the
possible degeneration taken into account.
