En The aim of this work is to: (a) to highlight developments in the recognition of indigenous peoples’ rights in a particular American country, Argentina; (b) to point out some of the problems that this recognition has caused in that country, together with points which may contribute to its solution. The focus will be on the right to property and the so-called ‘right to one’s own law’. On that basis, it is suggested that the possible points of contact between the universality-multiculturalism debate in Europe and the debate in Latin America on indigenous rights should be further studied.