The spectral and angular distributions for the Compton effect in a constant electro-magnetic field are obtained. The possibility of the existence of the induced Compton scattering in an external field (i.e. two-photon emission, one of the two photons being induced by the incident wave) is demonstrated. In the case of a constant magnetic field the deviation from the Klein-Nishina formula of the obtained distribution for the Compton effect as well as the behaviour of the distribution for the induced Compton effect are discussed. The optimal region of the parameters for the possible experimental test of these effects is given.