  We present the Complex Envelope Variable Approximation (CEVA) as the very
useful and compact method for the analysis of the essentially nonlinear
dynamical systems. It allows us to study both the stationary and non-stationary
dynamics even in the cases, when any small parameters are absent in the initial
problem. It is notable that the CEVA admits the analysis of the nonlinear
normal modes and their resonant interactions in the discrete systems without
any restrictions on the oscillation amplitudes. In this paper we formulate the
CEVA's formalism and demonstrate some non-trivial examples of its application.
The advantages of the method and possible problems are briefly discussed.
