The photoelectromagnetic (PEM) effect occurs in a solid when the diffusion currents of excess carriers away from an illuminated surface are deflected by a magnetic field to give a net current parallel to the surface. The effect has been studied in a number of semiconductors, providing information about carrier recombination and transport; recently, PEM responses were obtained in some semimetals. The present paper extends earlier theories of the effect in order to treat the cases of many-valleyed solids, and at the same time the transfer of excess carriers between electron or between hole valleys (intervalley scattering) is taken into account in addition to the transitions from electron to hole valleys (recombination). The possibilities of experimental determination of recombination and intervalley scattering times for various crystal orientations are discussed. Apparently it is often possible to choose an orientation which provides a determination of recombination time independent of the intervalley scattering time, but the reverse is not true, and even for extremely simple band models a reasonably precise determination of scattering time through the PEM effect seems difficult.