In semiconductors with extremely low majority carrier densities, the conductivity of the surface space charge region can be very different from the conductivity of the bulk. This paper demonstrates that the conductivity of this surface space charge region can be materially altered by the application of a magnetic field which is perpendicular to the direction of current flow. A tentative prototype model of this effect is presented which not only illustrates the mechanisms of importance, but also is sufficiently accurate to enable one to estimate the order of magnitude of the effect for certain experimental conditions. This model suggests that this effect may find application in magnetoresistance and/or negative resistance devices and might prove useful in the measurement of surface parameters.