This thesis seeks to explain cross-sectoral variation in convergence with EU rules in countries outside the EU that lack regulatory capacities and democratic development. In contrast to accounts predominant in the Europeanization literature, this study presents evidence to suggest that regulatory change in non-accession countries is not doomed to failure despite high initial adaptation costs that cannot be mitigated by EU membership conditionality. Making use of qualitative research methods, I analyze variation in convergence with EU rules in Ukraine across four policy sectors (corporate governance, technical regulation, telecommunications and food safety). I find that cross-sectoral variation is a function of different patterns of transnationalization that can be deep, shallow or mixed, depending on the properties and combined effects of interactions between domestic and external actors. In policy sectors where the combined effects of strong economic conditionality, strong market incentives for European and local firms and multiplex capacity building increase the incentives and capacities of domestic public and private actors for regulatory change, convergence with EU rules is likely to reach high levels thanks to deep patterns of transnationalization. My findings have the following implications. 1) Instead of high-powered political incentives (membership conditionality), the EU has down-to-earth economic incentives at its disposal (economic conditionality) to shape regulatory change in non-accession countries. Tying market access to convergence with EU rules in an unambiguous manner is necessary to achieve high levels of convergence beyond the EU’s borders. 2) Analyzing the combined effects of conditionality, markets and capacity building is more fruitful for explaining cross-sectoral variation in convergence with EU rules than isolated analyses of each mechanism. 3) Convergence with EU rules is not just about creating another level of hierarchy in the markets and political systems of target countries. Rather, it is about creating institutions for governance arrangements in which public and private actors coordinate regulatory tasks. Hence, transnational interactions need to increase the incentives and capacities of public and private domestic actors for high levels of convergence. 4) In countries like Ukraine, Russia is not a countervailing hegemon that unfailingly seeks to obstruct convergence with EU rules. Rather, Russia should be conceived of as an adapative hegemon that promotes or obstructs convergence depending on the interests of Russian business.