The objective of this Thesis is to comprehend Brazilian states’ role in intergovernmental relations in Brazil. Particularly, its goal consists in analyzing if they can perform a state coordination role, as federal government does in some federations aiming to reduce diversities, mainly, socioeconomic and institutional ones. This relationship is analyzed in education because the Federal Constitution of 1988 determines that states and municipalities must share competences in elementary education and they must cooperate in this level. However, the trajectory of this policy is characterized by a great variety in enrollments and in cooperation between Brazilian states and municipalities, which was never regulated. The research has involved the understating of the trajectory of educational policy, the National Education System, the relations between states and municipalities in this policy, the results of cooperation in municipal education policies in four states – Ceará, Mato Grosso do Sul, Pará e São Paulo – and on students’ performance. As a result, there are different models of cooperation between subnational governments in education, in which only the Ceará case is characterized as a state coordination one.