We predict the existence of negative differential resistance in nonresonant tunneling through a single barrier when a magnetic field is applied perpendicular to the current. Moreover, the use of a transfer Hamiltonian method for the calculation of the tunneling current allows the clear understanding of the physical origin of the experimentally observed oscillations as a function of the magnetic field. These two phenomena are consequences of the existence of individualized tunneling channels connected with anticrossings in the dispersion relation. © 1989 The American Physical Society.39151118711190