This paper assesses the time to radiation (radiotoxicity) and radiological (radiation risk) equivalence between natural uranium and radioactive waste of thermal and fast reactors at an increasing content of Np, Am, and Cm in radioactive waste. We calculate radiation risk by adapting models of the ICRP and other international organizations for the Russian Federation, taking into account background epidemiological indicators including cancer incidence, cancer mortality, and overall mortality. The radiation risk of internal exposure considers both the time after radionuclide intake and equivalent dose dynamics in human organs and tissues. To determine the time to radiological equivalence, we estimate the lifetime attributable risk of a single intake of natural uranium radionuclides and radioactive waste. An increase in the Np, Am, and Cm content of radioactive waste within 0.1–0.4% causes no effect on the radiological equivalence time, equal to ~100 years. However, a further increase from 0.5–0.8% prolongs the time to 300 years. A problem for optimizing the time to radiological equivalence is posed providing for waste storage costs and content of Np, Am, and Cm in long-lived radioactive waste.