Non-linear effects of QED multiple-photon processes on cyclotron spectra

The relativistic magnetic resonant multiple-photon processes are discussed up to order alpha(f)exp 2, in particular two-photon scattering and two-photon emission. The latter also contributes to the opacity and photon production, although more weakly than the scattering. These processes are nonlinear in the radiation field, and therefore the transfer depends sensitively on the cross sections. We show model spectra including three cyclotron harmonics for the accreting pulsar Her X-1 and the gamma-ray burster GB880205. The lines are highly polarized, and their depth is sensitive to the polarization treatment.