The theory of Allis and Rose based on the hypotheses of congruence and proportionality is used to formulate the problem of ambipolar diffusion and drift of a plasma of added carriers in a semiconductor in the presence of a magnetic field. These hypotheses together with the linearized equations for the particle flow densities of the electrons and holes permit an expression for the particle flow density of the added carriers to be derived. In its final form this expression is composed of a drift and diffusion term in which the ambipolar group mobility and diffusion coefficient appear as tensorial quantities. These antisymmetric tensors will reduce to the scalar quantities of van Roosbroeck (1953) when the magnetic field is set equal to zero and to the proper tensorial quantities for the added minority carriers in strong extrinsic n or p type semiconductors. Finally, as an illustrative example, the ambipolar continuity equation for the particle density of added carriers is solved as an initial-value problem in an unbounded domain in order to analyze the space and time behaviour of a pulse of added carriers whose initial distribution is a Dirac delta function.