An implication of nonzero neutrino masses is the existence of neutrino magnetic moments, which arise in extensions of the Standard Model. Among the whole set of electromagnetic properties, these physical quantities have received much attention, both theoretically and experimentally. In the present paper we review the contributions to neutrino magnetic moments from new physics described by a leff-right model, with Majorana neutrinos, which might be as large as 10(-11) mu B. These electromagnetic moments depend on Majorana phases. It turns out that, in presence of CP violation, specific sets of values of these phases can cancel up to two magnetic moments, while the remaining one must necessarily be nonzero and large.