  We study spin fluctuations in the spiral phase of the two-dimensional Hubbard
model at low doping on the basis of the spin-particle-hole coherent-state path
integral. In the strong correlation limit, we obtain an analytical expression
of the spin-wave excitations over the entire Brillouin zone except in the
vicinity of ${\bf q}=0$. We discuss the validity of the Hartree-Fock and
random-phase approximations in the strong-coupling limit, and compare our
results with previous numerical and analytical calculations. Although the
spiral phase is unstable, as shown by a negative mean-field compressibility and
the presence of imaginary spin-fluctuation modes, we expect the
short-wavelength fluctuation modes (with real energies) to survive in the
actual ground-state of the system.
