The development of light, neutron-rich beams has opened new perspectives for the study of many-neutron systems in the last decade. Breakup experiments at GANIL are described, using beams of (6,8)He, (11)Li, (14)Be and (15)B at several tens of MeV/N. Our approach is based on the detection in coincidence of the breakup fragment and the neutrons in order to investigate the different correlations in the final state of these very neutron-rich systems, in particular, 2n correlations in (6)He, (11)Li and (14)Be, three-body correlations in (14)Be, and 4n correlations in (8)He and (14)Be.