In this paper we investigate tax competition in a neoclassical growth model where each country may use both residence- and source-based capital taxes. We show that both types of capital taxes are zero at any interior steady state, just as in a closed economy. For symmetric countries, and even for countries that differ only with respect to size and productivity, we prove analytically and verify numerically that the open-economy policies coincide exactly with the closed-economy policies in all time periods. For countries that are asymmetric in other dimensions, we find that source-based taxes are used to manipulate the intertemporal terms of trade in the short run. Either way, the fiscal externalities of source-based taxes vanish once residence-based taxes are allowed.