The issue of stability of superhalogen anions in an aqueous solution is investigated on the basis of theoretical calculations carried out at the CCSD(T)/6-311++G(d,p)//MP2/6-311++G(d,p) level for two representative negatively charged systems (NaF2- and AlF4-) whose fragmentation products differ in polarity. The presence of a water solvent is simulated independently by employing the polarized continuum solvation model and by involving eight H2O molecules explicitly to allow interactions at the molecular level. The best estimates of the Gibbs free energies characterizing the AlF4- and NaF2- fragmentation reactions in a water solvent are evaluated as equal to 33-34 and 12-14 kcal/mol, respectively (assuming the F- and AlF3/NaF products) or 14-15 and 26-28 kcal/mol, respectively (assuming the HF and AlF3OH-/NaFOH- products). The corresponding fragmentation routes are suggested to be nonoperative at T = 298.15 K. The conclusion concerning the thermodynamic stability of the AlF4- and NaF2- superhalogen anions in the aqueous phase is formulated and discussed.