At low and moderate levels of government debt, there appears to be little relation between the level of debt and its maturity. But at high levels of debt, a strong inverse relation emerges. We start the paper by documenting this inverse relation for those OECD Countries which have reached very high levels of debt. We then provide a theory of the joint movements of debt and maturity which can explain both sets of facts. It is based on the idea that, at high levels of debt, the government may need to decrease the maturity of the debt as debt increases, in order to maintain the credibility of its anti-inflation stance.