Optimal nonlinear taxation of income and savings is considered in a two-period model with two individuals who have additively separable preferences and who only differ in their skill levels. When the government can commit to its second period policy, taxes on savings do not form part of the optimal tax mix. When commitment is not possible, the optimal tax scheme distorts private savings behavior. If the types are separated in period one, it is optimal to tax the savings of the high-skilled individual and to tax the savings of the low-skilled individual at a lower, possibly negative, rate. If the types are pooled in period one, it is optimal for the low-skilled (high-skilled) individual to face a marginal savings tax (subsidy). In both cases, the savings of the high-skilled individual are distorted because this individual rationally expects that some of his savings will be redistributed to the low-skilled individual in the second period. The savings of the low-skilled individual in the separating case are taxed at a lower rate so as to relax an incentive compatibility constraint.