The computer code MINEQL was adapted and extended to assess the solubility and speciation of radioactive waste nuclides in groundwaters under conditions which are expected to exist in the surroundings of planned underground repositories. By means of an additional data base including standard reaction enthalpies and heat capacities at 25 degrees C, the relevant equilibrium constants at 25 degrees C can be converted to other temperatures using Ulich's formulae. The activity coefficients for dissolved species are modelled with a temperature dependent function of the Davies' approximation type. The report is segmented in three main parts: (1) a review of the MINEQL fundamentals and a summary of the theory needed for the extensions; (2) an outline of the general programme structure and of criteria applied to the selection of thermodynamic data; (3) a discussion of the results from first model applications to evaluate the solubility and speciation of U, Pu, Np and Th in two Swiss groundwaters, based either on the approach of negligible chemical disturbance or on a solid/solution titration concept. All thermodynamic data involved in this study are collected in an appendix, together with a compilation of references.