Presents the Principle of Due Process of Law in the Constitution of the Federative Republic of Brazil of 1988 and its legal nuances. This legal norm radiates effects in the field of Criminal Procedural Law, since the Ius Puniendi must observe legality and the set of coordinated acts that are realised with the Principle of the adversarial process. Thus, Ronald Dworkin’s theoretical framework, which originated in the United States and therefore has a common law hue, is evidenced in the Constitution and Constitutionalised Criminal Procedure in a democratic republic.