The characteristics of hot-carrier magnetoresistance for small magnetic fields are studied with the assumptions: (a) The constant-energy surfaces are spherical and carriers are scattered by acoustic and optical phonons; and (b) the constant-energy surfaces are ellipsoidal and the scattering is due to acoustic, optical, and intervalley phonons. It is shown that for a spherical constant-energy-surface model the magnetoresistance has a small negative value decreasing with increasing field, and the magnetoresistance coefficient is independent of the field if the scattering is by acoustic phonons alone. On the other hand, for predominant optical-phonon scattering the magnetoresistance and also the magnetoresistance coefficient are positive and decrease with increasing field. In the case of many-valley band structure as in n-type germanium, the characteristics of magnetoresistance and magnetoresistance coefficient for predominant acoustic-phonon scattering are the same as for a spherical constant-energy-surface model, but the sign is positive and the values are larger. The variation of magnetoresistance and magnetoresistance coefficient for predominant optical-phonon scattering when the electric field is in the  direction is similar to that for a spherical constant-energy-surface model, but the values are higher and the characteristic varies in details. For the  direction of the field, on the other hand, the magnetoresistance decreases with the field, but the magnetoresistance coefficient increases with the field. The values of magnetoresistance calculated from theory, assuming acoustic- and optical-phonon scattering, are found to agree closely with the experimental results. The inclusion of the effects of intervalley scattering leads to a further improvement in the agreement. © 1966 The American Physical Society.