Simultaneous consideration of the irradiation time and the cumulative dose is necessary for evaluating the risk of long-term exposure to radiation at low dose. This study intends to examine several numerical relationships between doses and dose rates in biological responses to gamma radiation. Data on inhibition of [3H] thymidine uptake and micronucleus formation in human osteosarcoma cells were analyzed using the median effective dose (MED) as a measure of the risk. MEDs were calculated using parameters estimated by fitting general logistic curves to the dose-response relationships for each group defined by irradiation time. Both biological responses, the inhibition of [3H] thymidine uptake and micronucleus formation, decreased sharply when the dose rates were less than 0.01 Gy/h. Exponential functions were fitted to the log relationships between MEDs and dose rates. This modified exponential model described well the quantitative effect of dose rates on MEDs, and suggested that risk is extremely low at very low dose rates.