Abstract : The unbound neutron-rich systems 10,12Li and 13Be have been investigated via breakup of 15B at 35 MeV/nucleon. The lifetimes of such unbound nuclei are so short (10−21 s) that they cannot be detected directly. Instead, the coincident detection of the charged fragment and neutron was employed to reconstruct the decay energy of the system. The interpretation of the decay spectra required the development of simulations which took into account the effects of the experimental setup and included the generation of the lineshapes of levels (virtual states and resonances) as well as the construction of an uncorrelated background. The results of the simulations were compared to the reconstructed decay energy spectra and the method tested using the data obtained for the well known system 7Heg.s.. In the case of 10Li, the results indicate the presence of a virtual s-state with as = −10+6 −22 fm and a resonance (`=1) at Er=0,5±0,15 MeV with a width ¡=0,25 MeV. This conrms the inversion of the º1p1/2 and º2s1/2 levels observed in the less neutron-rich N=7 isotone 11Be. For 12Li, the results are consistent with an s-wave virtual state with a scattering length of as · −3 fm. Finally, a very narrow peak observed just above threshold in the 12Be+n decay energy spectrum was identied as arising from the process 15B!14Be¤(2+)!12Be+n+n, rather than a virtual s-state in 13Be.