We investigate the coupled charge and spin collective excitations in the spiral phases of the two-dimensional Hubbard model using a generalized random-phase approximation. Already for small doping the spin-wave excitations are strongly renormalized due to low-energy particle-hole excitations. Besides the three Goldstone modes of the spiral state the dynamical susceptibility reveals an extra zero mode for low doping and strong coupling values signaling an intrinsic instability of the homogeneous spiral state. In addition, near-zero modes are found in the vicinity of the spiral pitch wave number for out-of-plane spin fluctuations. Their origin is found to be the near degeneracy with staggered noncoplanar spiral states which, however, are not the lowest energy Hartree-Fock solutions among the homogeneous spiral states. {copyright} {ital 1996 The American Physical Society.}