An expression for the surviving fraction of a replicating population of cells exposed to permanently incorporated radionuclide is derived from the microdosimetric-kinetic model. It includes dependency on total implant dose, linear energy transfer (LET), decay rate of the radionuclide, the repair rate of potentially lethal lesions in DNA and the volume doubling time of the target population. This is used to obtain an expression for the biologically effective dose (BED_α/β) based on the minimum survival achieved by the implant that is equivalent to, and can be compared and combined with, the BED_α/β calculated for a fractionated course of radiation treatment. Approximate relationships are presented that are useful in the calculation of BED_α/β for alpha- or beta-emitting radionuclides with half-life significantly greater than, or nearly equal to, the approximately 1-h repair half-life of radiation-induced potentially lethal lesions.