This technical note considers global cooperative output regulation for a class of heterogeneous nonlinear multi-agent systems. By using the internal model principle and the adaptive control technique, a novel distributed adaptive control scheme is developed. Contrary to most existing results, the proposed controller is applicable to multi-agent systems with agents of non-identical relative degrees and non-identical unknown control directions under a general digraph. Moreover, any existing Nussbaum-type functions can be adopted in the proposed control scheme, and the adopted Nussbaum-type functions can be nonidentical for each agent. It is shown that global cooperative output regulation of the controlled multi-agent system can be achieved under some mild assumptions. A numerical example is finally presented to illustrate the effectiveness of the proposed controller.