Human blood was irradiated with accelerated ions: 20 MeV 4He, 425 MeV 12C and 1480 MeV and 996 MeV 16O. For each ion, the blood was exposed to a range of doses as thin specimens in the track segment mode, so that irradiations took place at nearly constant LETs of 31.4, 61, 52 and 69 keV μm-1, respectively. Lymphocytes were cultured to the first in vitro metaphase, analysed for chromosomal damage and the dicentric aberration frequencies fitted to the linear quadratic model of dose-response. For these high LET radiations, the linear (α) yield coefficient predominated and increased with LET, at least up to 60 keV μm-1. Apart from the 996 MeV oxygen ions, the data indicated the presence of a quadratic (β) coefficient, statistically consistent with values obtained with low LET radiations. However, the associated uncertainties on the measured β values were large, illustrating the general problem that β is more difficult to measure against a dominating and ever-increasing α term. The existence or otherwise of a β component of the dose-response at these radiation qualities has important consequences for modelling mechanisms of aberration induction by radiation.