  We calculate spectra of magnetic excitations in the spin-spiral state of
perovskite manganates. The spectra consist of several branches corresponding to
different polarizations and different ways of diffraction from the static
magnetic order. Goldstone modes and opening of gaps at zero and non-zero
energies due to the crystal field and the Dzyaloshinski-Moriya anisotropies are
discussed. Comparing results of the calculation with available experimental
data we determine values of effective exchange parameters and anisotropies. To
simplify the spin-wave calculation and to get a more clear physical insight in
the structure of excitations we use the {\sigma}-model-like effective field
theory to analyze the Heisenberg Hamiltonian and to derive the spectra.
