  We analyze the properties of magnons in metallic electron systems with spiral
magnetic order. Our analysis is based on the random phase approximation for the
susceptibilities of tight binding electrons with a local Hubbard interaction in
two or three dimensions. We identify three magnon branches from poles in the
susceptibilities, one associated with in-plane, the other two associated with
out-of-plane fluctuations of the spiral order parameter. We derive general
expressions for the spin stiffnesses and the spectral weights of the magnon
modes, from which also the magnon velocities can be obtained. Moreover, we
determine the size of the decay rates of the magnons due to Landau damping.
While the decay rate of the in-plane mode is of the order of its excitation
energy, the decay rate of the out-of-plane mode is smaller so that these modes
are asymptotically stable excitations even in the presence of Landau damping.
