[en] We extend the study of multiphonon excitations in heavy ion collisions to the case of the pygmy resonances. The motivation of this study relies in our findings on multiphonon investigation [2] at low energy excitation. Indeed, we have found that a few low lying multiphonon states are excited in a heavy ion collision process with a quite strong probability. These states lay in the region of the pygmy resonances and the question is whether they may contribute to the observed peak. Starting from a microscopic approach based on RPA, mixing of two-phonon states among themselves and with one-phonon states is considered within a boson expansion approach with Pauli corrections. By diagonalizing a quartic microscopic Hamiltonian in the space of one-, two- and three-phonon states we generate mixing eigenstates with an anharmonic spectrum. Non linear terms are also taken into account in the external mean field of one of the nuclei which is responsible of the excitation of the other partner of the reaction. The inelastic cross section are calculated by solving semiclassical coupled channel equations, the channels being superpositions of one-, two- and three-phonon states. The calculations have been done for two different Skyrme interaction (SGII and SLY4) and for the reactions A^Sn + 2^08Pb at 500 MeV/A. We found an increase of the cross section in the low lying PDR energy region which is mainly due to the excitation of several states whose population is strongly suppressed by selection rules when anharmonicities and non-linearities are neglected. The increase varies from 3% up to 21% depending on the isotope considered and the Skyrme force used. In general, the SLY4 interaction produces a smaller anharmonicity which is then reflected in a lower increase of the cross section in the PDR region. On the contrary, the results obtained with the SGII show the importance of anharmonicities and non linearities for the study of the PDR. The pygmy resonance is much more evident in nuclei with neutron skin and it is thought to be generated by the oscillation of the neutron in excess with respect to the core. To the discussion whether or not this mode is a collective one we have contributed with a novel analysis based on the investigation of the coherent construction of the reduced transition probability which should unambiguously give an answer to this problem. Our results show that although the degree of collectivity is not as high as the one of the GDR, they are far to be considered as due to one p-h configuration. Indeed, while for the GDR, as it is very well known, many configurations contribute appreciably and add up coherently, in the PDR case there are several configurations contributing but some of them cancel out so that, finally, the reduced transition probability B(E1) is quite smaller than what one should get without such cancellations and of the same order of a single p-h configuration.(author)