The current international paradigm on the biological effects of radiation is based mainly on the effects of dose with some consideration for the dose rate. No allowance has been made for the potential influence of a changing dose rate (second derivative of dose), and the biological effects of exposing cells to changing dose rates have never been analyzed. This paper provides evidence that radiation effects in cells may depend on temporal changes in the dose rate. In these experiments, cells were moved toward or away from an X-ray source. The speed of movement, the time of irradiation, and the temperature during exposure were controlled. Here we report the results of the first experiments with TK6 cells that were exposed at a constant dose rate, at an increasing dose rate, or at a decreasing dose rate. The average dose rate and the total dose were same for all samples. Micronuclei were scored as the end point. The results show that the level of cytogenetic damage was higher in cells exposed to a decreasing dose rate compared to both an increasing and a constant dose rate. This finding may suggest that the second derivative of dose may influence radiation risk estimates, and the results should trigger further studies on this issue.