Over and over again, history shows that countries default on external debt when their economies experience a downturn. This paper presents a theoretical model of international lending that is consistent with this evidence. Productivity is stochastic and international capital markets are incomplete in two ways: the only internationally traded assets are non-contingent real bonds and borrowers cannot commit to repay loans. Low productivity realizations get carried forward through low investment that lower output and consumption and eventually result in self-fulfilling or solvency debt crises. When lenders are atomistic, self-fulfilling crises may arise for intermediate debt levels that would not trigger a default with a large lender. Alternative reforms to eliminate liquidity crises are analyzed. An international lender of last resort can eliminate liquidity crises provided it implements full bailouts via purchasing debt at its market price.