  This article proposed a new approach to the determination of the spectrum for
nonlinear continuous operators in the Banach spaces and using it investigated
the spectrum of some classes of operators. Here shows that in nonlinear
operators case is necessary to seek the spectrum of a given nonlinear operator
relatively to another nonlinear operator. Moreover, the order of nonlinearity
of examined operator and operator relatively to which seek the spectrum must be
identical. Here provided different examples relative to how one can find the
eigenvalue and also studied solvability problems.
