  We search for nonlinear effects in nuclear giant resonances (GRs), in
particular the isovector dipole and the isoscalar quadrupole modes. To that
end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF)
dynamics using Skyrme forces. Based on TDHF calculations over a wide range of
excitation amplitudes, we explore the collectivity and degree of harmonic
motion in these modes. Both GR modes turn out to be highly harmonic in heavy
nuclei from A=100 on. There is no trace of a transition to irregular motion and
multiple resonances are predicted. Slight anharmonicities are seen for light
nuclei, particularly for $^{16}$O. These are mainly caused by the spin-orbit
splitting.
