The purpose of the present work was to estimate the parameter 'a' describing the generalised equivalent uniform dose (gEUD) for tumours and its dependence on radiobiological parameters. The consequences of uncertainties in a on the gEUD were also studied. An estimate of a was found by requiring that, for a given target dose distribution, the mechanistic EUD (based on radiobiological linear quadratic modelling) equals gEUD. The estimate of a was found to depend on the dose distribution, and decreased with factors that increase the slope of the cell survival curve (i.e. decreasing alpha/beta values and increasing alpha values). Furthermore, the parameter a was estimated for 35 prostate cancer IMRT plans of varying dose distributions, for two sets of previously published radiobiological parameters: (1) alpha=0.15 Gy(-1) and alpha/beta=3 Gy, and (2) alpha=0.26 Gy(-1) and alpha/beta=10 Gy. The estimated values of a ranged from -25.6 to -22.4 for all combinations of dose distributions and parameter sets. Uncertainties in a were found to give only small uncertainties in gEUD. Although the current work shows limitations of the gEUD model for tumours, gEUD may still be preferable for biological treatment plan optimization, evaluation and reporting.