In this paper, a description of a new method for obtaining a strongly nonlinear analytic model for nonlinear electron devices is given. Specific examples include crossed‐field amplifiers and gyro‐travelling wave tubes. This method is an extension of previous work where a nonlinear partial differential equation is derived and reduced by a multiple time scales perturbation technique to a nonlinear Schrodinger equation. The extension of the above approach to a strongly nonlinear regime is accomplished by includingErfxB0(rf electric and dc magnetic field) effects in the linear dispersion relation in an approximate manner. The inclusion of theseErfxB0terms results in nonlinear coefficients (i.e., dependence uponErf) of the nonlinear Schrodinger equation. The importance of these rf related terms is discussed for the crossed‐field amplifier and the gyro‐travelling wave tube.