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Dynamic hysteresis in bistable amorphous wires is studied at frequencies up to 200 kHz. As frequency is increased, the magnetization loop exhibits progressive widening, maintaining its bistable property. The switching process is analyzed within the Neel-Brown theory of the magnetization reversal due to activation over an energy barrier. The frequency dependence of the switching field is evaluated by considering a "waiting time" for closure domain wall to escape the pinned state, which gives a very good agreement with the experiment. The time of the magnetization reversal decreases with frequency down to few microseconds at 200 kHz, owing to the switching field increase.