The aim of the paper is to overcome the culturalist approach and the dichotomy “tradition-modernity” in the study of Muslim minorities in Europe and, in particular, in the diagnostic of predictors for the shift of a tiny minority towards jihadist terrorism through violent salafism. The paper presents a series of biographical interviews of “new” Muslim migrants, mainly from Maghrebian countries –both potential migrants from Muslim countries (persons who are about to migrate) and immigrants in France, Italy and Spain that have arrived in the last ten to fifteen years. Fifty interviews with Maghrebian migrants or potential migrants have been collected in Algeria, Morocco, Tunisia, France, Belgium, Italy and Spain by a research group of the University of Paris VIII. 25 interviews with immigrants from Africa in Italy have been collected by the University of Florence team in the project PRIMTS. Far from expressing rejection in face of the West and Western values, far from expressing any form of nostalgia for the “tradition”, the eighty-five biographical interviews reveal a largely positive image of Europe.