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Tunneling phenomena in crossed electric and magnetic fields cannot be properly described using the one-band effective-mass approximation. For this purpose, the two-band Hamiltonian is solved in the presence of crossed electric and magnetic fields and also in parallel fields. For crossed fields, two types of solutions are obtained. The first, for E g /2m ¥ c % ) ll2 i are of the harmonic-oscillator type, with quantized energy levels. In this region there is no interband tunneling in a pure material. In the region of high electric field, where E>H (& g /2ni*c 2 ) 1/2 , the solutions are of the electric-field type with a continuous energy spectrum. The analogy of this model to the motion of free classical relativistic electrons in crossed fields is discussed. WKB solutions in the region of high electric field are used to calculate tunneling (Zener) current and photonassisted tunneling [Franz-Keldysh (FK) effect]. The Hamiltonian is solved to obtain quasistationary solutions, neglecting a term which acts as the perturbation causing the Zener tunneling. The tunneling integrals are computed by the method of steepest descent. The results are nearly identical to those of Aronov and Pikus, obtained by a different method. In general, the magnetic field decreases both Zener and FK tunneling. The result for Zener tunneling predicts that the current will depend on E and H approximately as exp(-H 2 /E 3 ), in good agreement with experiment. In the FK effect, for photon energies close to that of the gap, the ratio of the absorption in crossed fields to that at H~Q varies with frequency and field approximately as exp[-(& g -~n g . The ratio of the absorption in parallel fields to that at H=0 varies approximately as exp [-(& g -hca) l/2 H/E% The result for Zener tunneling predicts Qxp(-H/E) behavior, in contrast to exp(-H 2 /E s ) for crossed fields. The model in the preceding paper does not predict any Zener tunneling.