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We propose a rational expectations framework for understanding speculative hyperinflations that end in response to 'orthodox' stabilization programs. Motivated by a strong degree of hysteresis in the stock of real balances after the end of hyperinflations, we provide a cash-and-credit model in which the money demand exhibits persistence because individuals can establish long-lasting credit relationships. We use the model to show that if hysteresis in real balances is possible then a fiscal-monetary reform that successfully stops a speculative hyperinflation may fail to prevent it. We argue that speculative hyperinflationary equilibria are consistent with some key stylized facts observed in extreme hyperinflations.