The results of some new QED calculations are presented. We consider two-photon emission by electrons, and determine magnetic field, spin and polarization dependence of the transition rates. We utilize the electron wave functions of Sokolov and Ternov (1968, Synchrotron Radiation, Berlin: Akademie), rather than those of Johnson and Lippmann (1949, Physical Review D, 76, 828). As pointed out by Graziani (1993, Astrophysical Journal, 412, 351), use of the former wave functions is necessary to obtain results valid outside the weak field limit. The results are of particular interest for processes in magnetars, for which the magnetic field is near, or can exceed, the critical value(Bcr=4.414×1013&hthinsp;G).©2000 American Institute of Physics.