The assumption of a linear dose response used to describe the biological effects of high-LET radiation is fundamental in radiation protection methodologies. We investigated the dose response for chromosomal aberrations for exposures corresponding to less than one particle traversal per cell nucleus by high-energy charged (HZE) nuclei. Human fibroblast and lymphocyte cells were irradiated with several low doses of <0.1 Gy, and several higher doses of up to 1 Gy with oxygen (77 keV/μm), silicon (99 keV/μm) or Fe (175 keV/μm), Fe (195 keV/μm) or Fe (240 keV/μm) particles. Chromosomal aberrations at first mitosis were scored using fluorescence in situ hybridization (FISH) with chromosome specific paints for chromosomes 1, 2 and 4 and DAPI staining of background chromosomes. Nonlinear regression models were used to evaluate possible linear and nonlinear dose-response models based on these data. Dose responses for simple exchanges for human fibroblasts irradiated under confluent culture conditions were best fit by nonlinear models motivated by a nontargeted effect (NTE). The best fits for dose response data for human lymphocytes irradiated in blood tubes were a linear response model for all particles. Our results suggest that simple exchanges in normal human fibroblasts have an important NTE contribution at low-particle fluence. The current and prior experimental studies provide important evidence against the linear dose response assumption used in radiation protection for HZE particles and other high-LET radiation at the relevant range of low doses.