With the entry into force of the Federal Law of the Isim on January 1, 1948 established the tax with which the federation began the coordination of the tax system of trade and industry in Mexico through a gradual scheme whose progress depended on the signing of coordination agreements between said level of government and the federative entities, which jointly aimed to centralize the branch. This coordination scheme also sought to advance towards the establishment of a tax figure that relied exclusively on consumption (final transactions). In this context, the main objective of the present article is to explain this configuration of double transition implied in the isim, from the problems that the federation faced before its establishment. In this sense, we intend to understand the beginning of the coordination process in this area through the problem of the distribution of the tax authorities that arose between the federal and local tax authorities and the difficulties that the federation faced in order to establish immediately the tax on consumption.