A biophysical model has been applied to describe the production of exchange chromosomal aberrations (dicentrics) in human lymphocytes by radiations of different qualities. The model includes a detailed description of the energy deposition pattern in the form of computer-generated tracks. Energy deposition events are further converted to DNA double-strand breaks (DSBs). Formation of chromosomal exchanges is modeled in competition with repair in a distance-dependent manner with breaks in proximity being most likely to interact. We demonstrate that an assumption of an RBE > 1 for production of DSBs at higher LET leads to a significant increase with LET of both the linear and the quadratic coefficients of the dose response for exchange formation. The latter is not supported experimentally and argues against high RBE values for production of DSBs, at least for those breaks involved in chromosomal exchanges. Assuming that the RBE for production of DSBs is unity, the calculated dose-response curves conformed to experimental data for 60Co γ rays, 250 kVp X rays and 8.7 MeV protons. The linear coefficient for 23.5 MeV 3He ions is underpredicted. The model predicts that a quadratic term in the dose response for exchange aberrations should be observed at LET values of 20-30 keV/μm. The curvature is not observed experimentally, and the contradiction is discussed.