Motivated by the debt crisis in the world, we apply methods of stochastic control to study two problems related to government debt management. In the first problem, we consider a government that wants to control its debt ratio. The debt generates a cost for the country. The government can reduce its debt ratio, but there is a cost associated with this reduction. We apply the theory of stochastic singular control to obtain an explicit formula for the optimal government debt ceiling. In the second problem, we develop a theoretical model for optimal currency government debt portfolio and debt payments. We allow both government debt aversion and jumps in the exchange rates. We apply the theory of classical stochastic control to solve the optimal currency debt problem. [This is joint work with Ricardo Huaman-Aguilar].