After a short outline of the features of global crime and of the (mostly negative and exceptional) measures of prevention of global crime, the paper upholds the thesis according to which in order to prevent global crime we need more positive measures, capable to eliminate the deepest roots and the ultimate causes of crime, rather than mere individual restrictive measures which entail the risk to increase the reasons for more criminality and, eventually, a serious rethinking of the forms of public power towards a global society and a global system of also criminal justice.