The cession of the Brazilian sovereignty on the region, either total or partial, has been proposal for some. However, such hypotheses, in contrast of the imaginary one of many, are not restricted to the last decades. The presses European and North American recently have dedicated special attention to the subject, what it has called the attention some. To the eyes of other nations, in what it can have some logic, for us, Brazilians, it does not pass of one confronts public. Historically an object of covets for diverse international actors, is state they or not, with the end of the call Cold War and the dismemberment of the Soviet Empire the question of the Amaznia has come back to the international guideline with more frequency. The practical implementation of the Theory of the Hegemonic Stability, fact that if observed from the cited events, more seems to guarantee our unreliability, especially had the absence of a polar region of being able antagonistic enough strong to discourage desestabilizantes actions. Declarations made for influential personalities, in special of the call developed world, are especially preoccupying. American senator Al Gore declared in 1989: ‘ ‘

The Brazilians think that the Amaznia is of them. He is not. It belongs to all ns.’ ‘ Already French former-president Franois Mitterrand affirmed that: ‘ ‘ Necessary Brazil to accept a relative sovereignty on the Amaznia.’ ‘ The head of the agency of information of the American Armed Forces declared in 1998 that: ‘ ‘ In case that Brazil makes a use of the Amaznia that at risk puts the half-environment of the United States, we have to interrupt processo.’ ‘ With passing of the years, due not only to the increasing ambient problems faced by the humanity more also to the introduction of new concepts in the international system as of shared sovereignty, the question tends if to aggravate.