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Within the framework of coupled climate and economic systems our paper presents concepts provided by the (mathematical) “viability theory”. These include both the notion of “persistent evolutions” in a given environment, which maximize the exit time function of this environment as well as the evolutions obtained when their regulons are kept constant, and the notion of “heavy evolutions”, satisfying the inertia principle which dictates that regulons remain constant until their viability is at stake and then evolve with minimum velocity. Thus, in the case of coupled climate and economic systems, viability theorems provide all initial states at which emission levels of greenhouse gases are below a given threshold and for which economic changes are also below a given level of inertia.