Transsexualism may be considered as a gender identity disorder which is fundamentally characterised by the patient's deep dissatisfaction with his or her anatomical sex, and the desire to modify his or her body in such a way that it acquires the features of the other sex. Adult transsexuals have not often been the subject of psychoanalytical analysis; in fact, observations made regarding fetishist patients, transvestites or persons engaging in other perverse behaviour are often extrapolated to take in transsexuals. Stoller is an exception, having carried out important studies of this pathology from a psychoanalytical point of view. This paper, employing data collected on two transsexual patients, male and female, discusses whether transsexuality does indeed belong to the group of perversions, it speculates about the application of Stoller's dynamic hypotheses to the two cases presented and finally it analyses the expression of aggression in this pathology and the counter-transferential experiences it arouses, indicating possible directions for future study.