The process of historicization, that is the exportation of a European way of analysing societies focusing on their relations with the past and with time, a process so often studied and described in other parts of the world, had begun much sooner in the New World. In the XVIth century New Spain and Peru, historians, whether Spaniards, Mestizos or Indians, took up a double challenge: How to historicize Amerindian memories and societies? How to synchronize local times and memories with Christian European time and history? Or, to use the language of global history, with global Iberian time?