36 pages, 10 figures, 8 tables, 3 appendices.-- PACS nrs.: 27.20.+n; 24.70.+s.-- Printed version published Jul 15, 2007.Fragmentation reactions in a carbon target with beams of Li-11 and Be-14 at relativistic energies have been studied in a kinematically complete experiment at the ALADIN-LAND setup at GSI. Excited states in Li-11 and Be-14 were obtained from the data in the inelastic channel. The measured cross sections with the core nucleus in the final state show that in the Be-14 case core polarization plays an important role. In the one-neutron knockout channels the measured angular correlations between fragment and neutron are asymmetric, which demonstrates the presence of states with different parities in the Li-11 and Be-14 ground states. For Li-10 a low-lying virtual s-state, a p-state and evidence for a d-state could be extracted from the data, while the Be-12 + n system shows resonances with more complicated structure.This work was supported by the BMBF under Contracts No. 06 DA 115, No. 06 OF 838 and No. 06 MZ 864 I and by GSI via Hochschulzusammenarbeitsvereinbarungen under Contracts No. DA RICK, No. OF ELZ, No. MZ KRAK and partly supported by the Polish Committee of Scientific Research under Contract No. KBN/2P03B/144/10, CICYT under Contract No. FPA2005-02379 (MJGB, OT), RFBR under Contract No. 04-02-17251, EC under Contract No. ERBCHGE-CT92-0003, and under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No.W-7405-Eng-48. One of us (T.N.) is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation.Peer reviewed