The ionizing radiation dose-response relationships for internally deposited radionuclides are examined using data from humans involving Ra and laboratory animal studies involving alpha-emitters Ra, Ra, Ra, Th, Pu, Pu, and Am and beta-emitters Y, Sr, Y, and Ce. Intake routes included ingestion, inhalation, and injection. The lifetime effects are best described by three-dimensional average-dose-rate/time/response surfaces that compete with other causes of death during an individual's lifetime. Using maximum likelihood survival regression methods, the characteristic logarithmic slope for cancer induction was found to be about negative one-third for alpha-emitters or about negative two-thirds for beta-emitters. At the higher average dose-rates the principal deleterious effects were those associated with radiation-induced injury while at intermediate average dose-rates radiation-induced cancer predominates. The relative biological effectiveness for cancer induction of high linear energy transfer alpha radiation with respect to low linear energy transfer beta radiation is a strong function of dose-rate. As average dose-rate decreases, the effectiveness of the beta irradiation drops off more rapidly than that of the alpha irradiation. The cumulative dose yielding a specific level of induced cancer risk is less at lower dose-rates than at higher dose-rates showing an apparent inverse dose-rate effect (up to a factor of about 10 for high linear energy transfer alpha radiation and a factor of about 2 for low linear energy transfer beta radiation). The cumulative radiation dose is neither an accurate nor an appropriate measure of cancer risk associated with protracted ionizing radiation exposure. Cancer risk associated with protracted ionizing radiation exposure is a non-linear function of lifetime average dose-rate to the affected tissues. At low average dose-rates the long latency time required for radiation-induced cancer may exceed the natural lifespan. This long latency results in a lifespan virtual threshold (cancer risk p < 0.001) for each internally deposited radionuclide. For young adult beagles, bone sarcoma induction from alpha-emitting radionuclides was unlikely for cumulative doses below about 1 Gy (20 Sv) delivered specifically to the sensitive tissues at bone surfaces in a manner associated with radionuclide relative potency from highest for Th, Pu, and Pu to lowest for Ra. Bone sarcoma induction from ingested Sr was unlikely for cumulative beta radiation doses below about 20 Gy (20 Sv), but beta irradiation of tissues adjacent to bone also induced leukemia and soft tissue carcinomas above 10 Gy (10 Sv). Inhaled radionuclides tended to be most potent in producing lung carcinoma when the radiation dose was most uniformly distributed in the lung. In young adult beagles lung carcinoma from inhaled alpha-emitting Pu in the dispersible nitrate form was unlikely for cumulative doses below about 0.5 Gy (10 Sv) and below higher cumulative doses for other forms of Pu and Pu depending on relative potency. Lung carcinoma from inhaled beta-emitting Y in relatively insoluble fused aluminosilicate particles was unlikely for cumulative doses below about 5 Gy (5 Sv) and below higher doses for inhaled particles with Y, Ce, or Sr in order of decreasing potency.