A set of nonlinear dynamical equations for quadrupole and monopole mom
ents of nuclei is derived from the time-dependent Hartree-Fock equatio
n by using the so-called moments of the Wigner function. These equatio
ns make it possible to describe coupled large-amplitude monopole and q
uadrupole vibrations. The equations are solved numerically for Pb-208
and Ca-40 in a model involving separable farces. The giant quadrupole
and monopole resonances are reproduced quite well. A distinguishing fe
ature of this large-amplitude motion is the existence of multiphonon s
tates. They are analyzed in detail. Classical and quantum aspects of t
he analytically solvable one-dimensional purely monopole model are stu
died to clarify the problem of the anharmonicity of the collective spe
ctrum.