In this paper we investigate theoretically the effect of an external electric field on the rate constant of steady-state bulk diffusion-controlled reactions. We generalize previously derived results for isotropic diffusion in the absence of interparticle interaction [J. Chem. Phys. 87, 4622 (1987)] to the case where translational diffusion is anisotropic. A frequently occurring situation of transverse isotropy where D-x=D(y)not equalD(z) is considered in detail. We derive the first-order expansion for the reaction rate constant in terms of the electric field strength E, k(E)=k(0) (1+1/2epsilongamma), where gamma=k(0)/4piRD(perpendicular to), epsilon=qER/k(B)T, q is the charge, R is the contact distance, and D-perpendicular to is the transverse diffusion coefficient. Numerical calculations show that this first-order expansion works well in the whole range of applicability of the Nernst-Einstein relation, i.e., for epsilon<1. (C) 2004 American Institute of Physics.