There is strong evidence that biological response to ionizing radiation has a contribution from unirradiated "bystander" cells that respond to signals emitted by irradiated cells. We discuss here an approach incorporating a radiobiological bystander response, superimposed on a direct response due to direct energy deposition in cell nuclei. A quantitative model based on this approach is described for alpha-particle-induced in vitro oncogenic transformation. The model postulates that the oncogenic bystander response is a binary "all or nothing" phenomenon in a small sensitive subpopulation of cells, and that cells from this sensitive subpopulation are also very sensitive to direct hits from alpha particles, generally resulting in a directly hit sensitive cell being inactivated. The model is applied to recent data on in vitro oncogenic transformation produced by broad-beam or microbeam alpha-particle irradiation. Two parameters are used in analyzing the data for transformation frequency. The analysis suggests that, at least for alpha-particle-induced oncogenic transformation, bystander effects are important only at small doses-here below about 0.2 Gy. At still lower doses, bystander effects may dominate the overall response, possibly leading to an underestimation of low-dose risks extrapolated from intermediate doses, where direct effects dominate.