A model for tunneling in the presence of a localized, harmonic time-dependent potential is presented. The effect of dynamic oscillations on the static resonances is determined in two important cases: (1) two consecutive high barriers where resonances arise from potential energy traps, and (2) a sequence of random barriers where resonances arise from disorder-localized states. In both cases strong resonances survive even when the potential varies rapidly compared to the particles intrinsic lifetime. Analysis of the two-barrier case reveals an interesting connection to a solvable model of the incommensurate potential problem. © 1985 The American Physical Society.