The treatment of cancer using targeted radionuclide therapy is of interest to nuclear medicine and radiation oncology because of its potential for killing tumor cells while minimizing dose-limiting toxicities to normal tissue. The ionizing radiations emitted by radiopharmaceuticals deliver radiation absorbed doses over protracted periods of time with continuously varying dose rates. As targeted radionuclide therapy becomes a more prominent part of cancer therapy, accurate models for estimating the biologically effective dose (BED) or equieffective dose (EQD2_α/β) will become essential for treatment planning. This study examines the radiobiological impact of the dose rate increase half-time during the uptake phase of the radiopharmaceutical. MDA-MB-231 human breast cancer cells and V79 Chinese hamster lung fibroblasts were irradiated chronically with 662 keV γ rays delivered with time-varying dose rates that are clinically relevant. The temporal dose-rate patterns were: 1. acute, 2. exponential decrease with a half-time of 64 h (T_d = 64 h), 3. initial exponential increase to a maximum (half time T_i = 2, 8 or 24 h) followed by exponential decrease (T_d = 64 h). Cell survival assays were conducted and surviving fractions were determined. There was a marked reduction in biological effect when T_i was increased. Cell survival data were tested against existing dose-response models to assess their capacity to predict response. Currently accepted models that are used in radiation oncology overestimated BED and EQD2_α/β at low-dose rates and underestimated them at high-dose rates. This appears to be caused by an adaptive response arising as a consequence of the initial low-dose-rate phase of exposure. An adaptive response function was derived that yields more accurate BED and EQD2_α/β values over the spectrum of dose rates and absorbed doses delivered. Our experimental data demonstrate a marked increase in cell survival when the dose-rate-increase half-time is increased, thereby suggesting an adaptive response arising as a consequence of this phase of exposure. We have modified conventional radiobiological models used in the clinic for brachytherapy and external beams of radiation to account for this phenomenon and facilitate their use for treatment planning in targeted radionuclide therapy.