According to the present concept for final storage of spent nuclear fuel in Sweden, the spent fuel, encapsulated in copper or copper/steel canisters, will be placed in tunnels in a deep rock formation. The canisters will be surrounded by compacted bentonite clay acting as a buffer material. In connection with a safety analysis of such a storage facility, the total solubility of certain elements (e.g., uranium) as well as the transport properties (e.g., retardation due to sorption on mineral surfaces) of the long-lived radionuclides released from the canister have to be predicted or measured. The chemical conditions, governing the solubility and speciation of trace elements encountered in and around the repository depend on interactions between the ground water and the engineering materials in the repository and a production of oxidants due to radiolysis in the spent fuel. In the present study the speciation and solubility of uranium and neptunium in a bentonite-ground water system and in ground waters with compositions measured at a site at,~spr, SE Sweden, have been calculated. The calculations have been carried out using a recent version of the geochemical computer code PHREEQE and the database HATCHES 5.0, Predictions of the uranium and neptunium concentrations in the ground water in the vicinity of a damaged high level waste repository have also been performed. The uranium concentration in the water in the bentonite barrier is predicted to be of the same order of magnitude or lower than that found in some granitic ground waters. For neptunium the calculations are uncertain due to the small amount of experimentally determined thermodynamic data and few verifications under the conditions (pH -Eh -carbonate concentration) considered. The predicted concentrations (ca 10-12 m, corresponds to ca 0.006 Bq/1) may be regarded as high, considering the high toxicity of neptunium and its long half-life.