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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.