Abstract <p>A decomposition approach to mathematical modeling of nonlinear microwave devices with a distributed interaction has been developed based on descriptors of nonlinear autonomous blocks with Floquet channels (NABFs) in the form of nonlinear equations connecting the amplitudes of incident and reflected waves at the input cross section of Floquet channels. An iterative method for NABF decomposition has been developed based on the linearization of their descriptors. Using the computational algorithm developed by using the NABF method, the results of mathematical modeling of nonlinear diffraction and interaction of microwaves with nonlinear conducting and dielectric inclusions in striplines have been obtained.</p>