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. This substitution reaction followed by analysis of experimental data applying ANN (Artificial Neural Network) method was utilized for indirect determination of those anions and/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.