There is growing clinical interest in the use of ¹²⁵I (half-life 59.4 days) and ¹⁰³Pd (half-life 16.97 days) for permanent brachytherapy implants. These radionuclides pose interesting radiobiological challenges because, even with slowly growing tumours, significant tumour cell repopulation may occur during the long period taken to deliver the full radiation dose. This results in a considerable amount of the prescribed dose being wasted. There may also be changes in the tumour volume during treatment (due to oedema and/or shrinkage), thus altering the relative geometry of the implanted seeds and causing additional dose rate variations. This assessment examines the interaction between the above effects and additionally includes allowance for the influence of the relative biological effectiveness (RBE) of the radiations emitted by the two radionuclides. The results are presented in terms of the biologically effective doses (BEDs) and likely tumour control probabilities (TCPs) associated with the various parameter combinations. The overall BED enhancement due to the RBE effect is shown always to be greater than the RBE itself and is greatest in tumours which are radio-resistive and/or fast growing. The biological dose uncertainties are found to be less with ¹⁰³Pd and the TCPs associated with this radionuclide are expected to be significantly higher in the treatment of some 'difficult' tumours. Using typically prescribed doses ¹²⁵I appears to be better for treating radiosensitive tumours with long doubling times and which shrink fairly rapidly. However, unless ¹²⁵I doses are reduced, this advantage may well be offset by the greatly enhanced biological doses delivered to adjacent normal structures.