We report the existence of nonlinear eigenmodes, modes without an energy ex
change between composed harmonics, in waveguides with quadratic nonlinearit
y. It is shown that the necessary condition for the eigenmodes to exist is
the nonzero dispersion of the cladding materials. It is also demonstrated t
hat the fundamental field may form eigenmodes with the second-harmonic fiel
ds of two different magnitudes. The symmetry properties of found modes are
studied. (C) 2000 Elsevier Science E.V. All rights reserved.