The work is based on the question of whether and to what extent the use of armed forces to combat maritime piracy can be presented and justified as an exercise of extraterritorial criminal power. Based on the international and constitutional legal framework as well as the criminal theory foundations of state penal power, it shows that German criminal law covers the phenomenon of maritime piracy to a large extent. The scope of substantive criminal law also determines that of procedural law. Soldiers who are deployed on the high seas or in foreign coastal waters to combat piracy may therefore rely on certain standards of criminal procedural authority to the extent that they carry out criminal prosecution from a substantive and functional perspective.