A spectrophotometric determination of uranium(VI) in the presence of some ligands (hydrogencarbonate, oxalate, hydrogenphosphate) is proposed. Analyzing the spectrophotometric data by the principal component analysis, the formation of ternary complexes was proved at low concentrations of hydrogencarbonate and oxalate; however, they decompose and more stable binary complexes [UO₂L₃]^4? are formed in the presence of ligand excess. The substitution reaction followed by analysis of experimental data by the ANN (Artificial Neural Network) method was used for indirect determination of the above anions or simultaneous analysis of uranium(VI) and hydrogencarbonate/oxalate in their mixtures. This procedure was validated by analysis of mineral waters. The proposed method is precise (rsd < 5 %) and accurate and can be applied in speciation analysis of uranium(VI) in mineral waters.