Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v2/c2. The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished  in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is vE ≪ v, where v is the characteristic velocity of the particle. For a strong electric field, vE∼v. The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1-3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2-4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v2/c2, where c is the velocity of light. Also hf fields may be present. © 1982 Plenum Publishing Corporation.