Radioactivity induced in a typical fusion power reactor was calculated for all elements with atomic number Z ≤ 84 and for different irradiation times. It was shown that the shutdown activity varies widely with the duration of the irradiation time. In general, the activity induced by radionuclides with half-lives that are significantly longer than the period of irradiation increases with increasing the irradiation time. On the other hand, the level of activity generated by any radionuclide with a half-life which is significantly shorter than the reactor life-time reaches a peak early during irradiation and then may starts to drop to lower value before the end of irradiation. The severity of this peaking is determined by the destruction rate of the parent element. The activities generated by long-lived nuclides (important for waste management) in any fusion reactor with life time in the order of 30 years reach their peak values at end-of-life. In the mean time, using the activity and decay heat values generated by short and intermediate-lived radionuclides at the end of reactor life to represent the worst case values used in safety analyses related to a loss of coolant accident (LOCA) and accidental release of radioactive inventory might lead to a substantial underestimation of the results.