The paper focuses on the problem of electromagnetic TM wave propagation in a two-layered circular cylindrical dielectric waveguide (this is an example of Bragg’s waveguide) with a inhomogeneous nonlinear permittivity inside one of its layers, the other layer has a constant permittivity. The physical problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell’s equations. Eigenvalues of the problem correspond to propagation constants of the waveguide. Existence of eigenvalues of the considered problem is stated. Numerical experiments are carried out for three types of nonlinearities. Comparisons with linear/nonlinear inhomoge- neous cases are given.