With an observation of the stylized facts of the crisis-hit Asian countries, the paper presents the 'hyperbola of external debt' hypothesis contending that there may exist a threshold hyperbola warning a prospective occurrence of a currency crisis. The empirical evidence shows that given the financial fragility and others, a composite indicator for making a diagnosis on the health of the external debt position of a country is roughly the product, {the ratio of total external debt to GDP (%) - 10%}{the ratio of short-term external debt to total external debt (%) - 10%}.