[pt] O objetivo da presente dissertação é contribuir para o aprimoramento do debate que se trava, desde a promulgação da Constituição de 1988, sobre a cooperação preconizada pelo parágrafo único do artigo 23, como forma de se realizar as tarefas administrativas comuns a todos os quatro entes federados. Com efeito, avaliamos não só as competências contidas na atual Constituição - demonstrando que a competência comum é autônoma e, portanto, ao lado das demais, estabelece o regime atual de repartição constitucional de competências - como, também, as principais normas constitucionais relacionadas com as Cartas Políticas anteriores, com o intuito de construir um raciocínio que nos conduza ao modelo atual de cooperação advindo do acima mencionado parágrafo único do artigo 23. A partir daquela metodologia, constatamos que esse agir estatal cooperado estabelecido pela Constituição de 1988, não obstante possuir raízes nas Constituições anteriores, é inovador e contemporâneo, refletindo o regime cooperativo estatal de agir previsto nos artigos 91a e 91b da Lei Fundamental de Bonn, com a redação que lhes conferiu a reforma de 1969. A cooperação será voluntária até a edição da lei complementar anunciada pelo parágrafo único do artigo 23 da Carta de 1988. Após, será ela obrigatória, mas esta obrigatoriedade somente surtirá efeitos a partir do momento em que os entes federados façam a opção pelo agir integrado, ou seja, desde que optem por realizar as tarefas administrativas comuns de forma cooperada, pois aquela lei complementar não tem autorização constitucional para estabelecer normas que reflitam qualquer tipo de subordinação, já que isso violaria a autonomia política a eles constitucionalmente assegurada. / [en] The objective of this study is to present a contribution to the juridical debate over the issue of cooperation, between the Union, the states, the Federal District and the municipalities, to carry out common administrative functions assigned to federal, state and local governments. This legal discussion has been troublesome since the promulgation of the Federal Constitution of 1988, which introduced a provision, in the sole paragraph of article 23, to regulate the matter of cooperation between the four public entities comprised in the Federative Republic of Brazil. As a matter of fact, this study not only analyzes the power (or authority) granted by the Constitution of 1988, in common, to the four above mentioned public entities, but also evaluates provisions of former Brazilian Constitutions dealing with that subject to devise a legal perspective on the cooperative model introduced under the rule of the sole paragraph of article 23. Hence, it demonstrates that common power (or authority) is autonomous and constitutes, with other forms of governmental authority, part of the constitutional framework of separation of powers. Based on such premises the conclusion of this essay purports that, notwithstanding the fact that cooperation between public entities has its roots in past Brazilian constitutional regulations, the form of cooperative action designed by the Constitution of 1988 is innovative and up- to-date, reflecting the model of state cooperative form of action introduced in Germany, during the constitutional reform of 1969, through the discipline of articles 91a and 91b of the German Constitution. Cooperation between the Union, the states, the Federal District and the municipalities shall be voluntary until the enactment of a Supplementary Law prescribed in the rule of the sole paragraph of article 23 of the Brazilian Constitution. After the passing of such legislation cooperation shall became mandatory, if the public entities involved decide to carry out common administrative tasks in a combined fashion. It is to be noticed, however, that the Supplementary Law referred in the sole paragraph of article 23 shall not establish any kind of subordination or hierarchy between the Union, the states, the Federal District and the municipalities due to constitutional provisions granting political autonomy to each of those entities.