This paper examines the governance challenges created by AI agents operating across the European Union (EU) and the United States (US). It argues that agentic systems differ from traditional AI because they can pursue longer-term goals, invoke tools to access external resources and act across distributed digital environments with limited human supervision. These features create three transatlantic risks. First, misalignment may propagate across borders when agents pursue lawful or ordinary goals through unlawful or harmful means. Secondly, runtime tool invocation expands the security attack surface and reduces visibility over agentic action chains. Thirdly, dependence on foreign-controlled models, cloud infrastructure, APIs and data centers create sovereignty and accountability asymmetries. The paper shows that neither EU nor US law currently provides a complete framework for addressing these risks. It therefore examines legal alignment, Constitutional AI, and technical standards as complementary governance mechanisms that may support future transatlantic regulatory cooperation.