The text analyses the advantages and problems for the study of Latin American history resulting from the application of two approaches known as global history and transnational history, with special reference to the latter. It therefore considers, in the first place, the limits imposed by the State- Nation to the study of the past populations and the need to overcome the state approach, making reference to examples from two somehow extreme areas: international migrations and the history of the national statistics systems. The second and third parts focus on the doubts offered by global history, with special reference to its degree of novelty and usefulness in relation to classical methods like comparison and the theory of systems. Finally, and considering the need to combine scales of analysis of different level, an agenda of socio- demographic topics is proposed for which the global approach might be relevant.