The paper presents a set of results about how do advanced mathematics students (applying to be mathematics teachers) process with specific implication cases. The aim is to identify, if they exist, the kind of organisation in the use of logic in theirs evaluating the truth value of implications. Several types of implications were used, for identifying factors involved in the management of the premise. Students’profiles were defined depending on the orientation of their answers to factual not computable implications with (always) false premise: ‘Logic'(‘the assertionis true as the hypothesis is false’), ‘Relevance'(‘the assertion is stupid’, ‘non sense’), ‘Falseness'(‘hypothesis always false, then assertionfalse’), ‘ND'(non dominant type of answer). The profiles were related to answers to other types of implications, including computable (mathematical) implications, with premise always false or predicates false for some values (‘hors-sujets’: Legrand, 1990). Two populations were compared (107 students in 1999, 71 in 2001). Globally, the distribution of profiles was similar in the two groups; answers to most of mathematical items differ depending on the profile. The ‘logic’profile was the only one with stable correct responses: it was a minority. Profiles seem to be relatively stable individual properties, enabling some qualitative anticipation as regarding their answers to a series of tests. Even if advanced mathematics students were more logical than subjects questioned in psychology experiments, the frequency of inefficient profiles (‘falseness’and ‘ND’) led to discuss how profiles could be changed, through scholar teaching and during teachers training. (ZDM/Mathdi)