Eigenvalues and eigenfunctions of stationary TE waves for plane symmetrical nonlinear waveguides are studied. For a negative refractive index difference between the core and cladding (antiwaveguide) regions are found where a continuum of eigenfunctions exist in certain energy intervals. Such regions are interpreted as regions of stability. There is possible concentration of optical power in the core as well as in the cladding in these regions. Boundary values of propagation constants for nonlinear waveguides and antiwaveguides are obtained.