Introduction – 1 Competence-Competence principle in the International Arbitration – 1.1 The Competence-Competence principle doctrine – 2 Who decides first the competence? – 2.1 The positive and negative effects of the Competence-Competence principle – 2.2 Is the arbitrator’s decision ever subjected to judicial review? – 2.3 The recognition of the rule of priority by local courts – 3 The development of Competence-Competence principle under Brazilian Statutory Law – 3.1 Competence-Competence principle codified into Brazilian Statutory Law – 3.2 Remarkable case law: dispute between Petrobras and the Brazilian Oil & Gas Agency (ANP) – 3.2.1 The Brazilian Superior Court of Justice’s recognition of the applicability of the Competence-Competence principle to concession agreements – 3.2.2 The case – 3.2.3 The STJ’s decision – 4 Conclusion – References.