The paper presents a model intended to define and discuss the sustainability of external debts in “emergent markets.” The first sustainability condition is the existence of a maximum in the debt-output ratio. With some simple behavior hypotheses it is shown that sustainability depends on the initial debt-exports ratio, the rate of growth of exports and the country-risk premium. An endogenous country-risk premium gives room for multiple equilibrium. The model allows the discussion of vulnerability vis-a-vis financial shocks and the propensity of the economy to jump to unsustainable paths. The first sustainability condition is not a stringent one. Two additional sustainability conditions are added: a positive rate of growth and a minimum in the domestic absorption-output ratio. The discussion of multiple equilibrium, vulnerability and the potential instability of sustainability is then extended. JEL Classification: F34; F32.