The unbound nuclei He-9 and He-10 have been produced in proton-knockout reactions from a 280 MeV/u Li-11 beam impinging on a liquid hydrogen target at the ALADIN-LAND setup at GSI. Information on their nuclear structure has been obtained from the relative-energy spectra, He-8 + n and He-8 + 2n, employing reaction models incorporating the structure of Li-11. The (8H)e + n relative-energy spectrum is dominated by a strong peak-like structure at low energy, which may be interpreted within the effective-range approximation as the result of an s-wave interaction with a neutron scattering length of -3.17(66) fm. This spectrum also shows evidence for resonance states at 1.33(8) MeV and at 2.4 MeV above the He-8 + n threshold. It is argued that the s-state might not be the He-9 ground state. For He-8 + n + n, the analysis of the relative-energy spectrum gives two alternative possibilities for an interpretation: either a narrow resonance at 1.42(10) MeV (Gamma = 1.11(76) MeV) superimposed on a correlated background, or two overlapping resonances, a ground state at 1.54(11) MeV (Gamma = 1.91(41) MeV) together with an excited state at 3.99(26) MeV (Gamma = 1.64(89) MeV). The two possible interpretations are discussed. (C) 2010 Elsevier B.V. All rights reserved.