This paper synthesizes and extends the literature on the taxation of foreign source income in a framework that covers both green…eld and acquisition investment, and a general constraint linking investment at home and abroad for the multinational by introducing a cost of adjustment for the mobile factor. Unless the cost of adjustment is zero, the domestic tax on foreign-source income should always be set to ensure the optimal allocation of the mobile factor between domestic and foreign assets and should follow the classical rules in the literature; national optimality requires the deduction rule, and global optimality requires the credit rule. Only in the zero-cost case does exemption become optimal. Allowances can be set so as to ensure that domestic and foreign asset purchases are undistorted by the tax system: this requires a cash- ‡ow tax on domestic investment in the green…eld case, and a cross-border cash ‡ow tax on foreign investment in both cases. These basic results extend to various extensions of the model, notably (i) when a pro…t-shifting motive is present; (ii) to some extent, when a corporate income tax is in place. The introduction of tax administration costs into the model can explain the empirical trend towards use of the exemption regime.JEL Classi…cation: H25, F23