A theoretical and experimental study of the tunneling ionization of deep impurities in semiconductors has been carried out for high-frequency alternating electric fields. It is shown that tunneling ionization occurs by phonon-assisted tunneling which proceeds at high electric field strengths into direct tunneling without involving phonons. In the quasistatic regime of low frequencies the tunneling probability is independent of frequency. Raising the frequency leads to an enhancement of the tunneling ionization. The transition from the quasistatic limit to frequency-dependent tunneling is determined by the tunneling time which, in the case of impurities interacting with thermal phonons, is controlled by the temperature. In both the quasistatic and high-frequency Emits, the application of an external magnetic field perpendicular to the electric field reduces the ionization probability when the cyclotron frequency becomes larger than the reciprocal tunneling time.