The central role of epidemics in the excess mortality of Amerindians is the main argument put forward by the contemptuers of the genocide thesis. Does this mean that the colonists had nothing to do with this catastrophe? Even without claiming to rule on the general character of the various processes of colonization of America, it is possible to detect in each of them operations that can be qualified as genocidal, including by relating them to the restrictive criteria defined in 1948.