The incidence of post transplantation lymphoproliferative disorders (PTLDs) and other neoplasms in organ transplant patients is higher than in the non-transplanted population. This event is more frequent in older subjects, due, at least in part, to the immune dysfunction induced by immunosuppressants administered to prevent rejection. Alterations of the immune system mechanisms of protection against carcinogenesis appear to be the key role in the in the pathogenesis of these neoplasms. The data of our study on the incidence of neoplasms occurred during a long-term follow-up in an elderly population after they underwent cardiac transplantation. This study gives, also evidence of the favorable effect of physical activity programs on cardiorespiratory and psychomotor function.