We study Ramsey model for an open economy applied to the case of Brazil. We find optimal tra jectories of consumption, investment, capital stock and net foreign liabilities and, with this, analyze debt sustainability in Brazil. A new approach to capturing optimal tra jectories is presented. The main tools are the Stable Manifold Theorem and the Lambda Lemma, normally used in the field of dynamical systems.We study Ramsey model for an open economy applied to the case of Brazil. We find optimal tra jectories of consumption, investment, capital stock and net foreign liabilities and, with this, analyze debt sustainability in Brazil. A new approach to capturing optimal tra jectories is presented. The main tools are the Stable Manifold Theorem and the Lambda Lemma, normally used in the field of dynamical systems.