This paper proposes to use claims models as a reasonable and operative alternative in order to allocate CO2 emissions by countries (or groups), in the framework of multilateral negotiations and the fight against climate change. This framework has two characteristics which fits this type of claims models: a restrictive global endowment (the maximum world emissions permitted) and the excess of emissions (and demand) by countries. The proposed methodology consists on establishing some requirements that any admissible distribution solution should satisfy, examining a broad group of theoretical distribution solutions emerged from the specific literature and analyzing their application according to reasonable ordering criteria linked to equity and stability properties. The proposed theoretical framework is applied empirically to an analysis by groups of countries in the period 2010- 2050, using various world endowments from Meinshausen et al. (2009), together with claims forecasts associated with the RCP scenarios. The results obtained point out that for intermediate claims scenarios the solutions associated with the constrained equal awards (CEA) and α-minimal (α-min) solutions are typically selected. In particular, these two solutions are clearly equity-sensitive, where the efforts to be made by Asia and OECD are very important, as a whole, and especially in the case of the CEA. Given these circumstances, and the better balance between equity and proportionality associated to the α-min allocation methodology maybe that one would be more operative and acceptable. Keywords: Carbon emissions, claims problem, climate change policy JEL classification: D7, H4, H8, Q58, Q54