We wish to study optimal dynamic nonlinear income taxes. Do real-world taxes share some of their features? What policy prescriptions can be made? We study a two-period model, where the consumers and government each have separate budget constraints in the two periods, so income cannot be transferred between periods. Labor supply in both periods is chosen by consumers. The government has memory, so taxes in the first period are a function of first-period labor income, whereas taxes in the second period are a function of both first- and second-period labor incomes. The government cannot commit to future taxes. Time consistency is thus imposed as a requirement. The main results of the paper show that time-consistent incentive-compatible two-period taxes involve separation of types in the first period and a differentiated lump-sum tax in the second period, provided that the discount rate is high or utility is separable between labor and consumption. In the natural extension of the Diamond (1998) model with quasi-linear utility functions to two periods, an equivalence of dynamic and static optimal taxes is demonstrated, and a necessary condition for the top marginal tax rate on first-period income is found.