A DFT study with QST3 approach method is used to calculate kinetic, thermodynamic, spectral and structural data of tautomers and transition state structures of some N-hydroxy amidines. All tautomers and transition states are optimized at the B3LYP/6-311++g** and B3LYP/aug-cc-pvtz level, with good agreement in energetic result with energies obtained from CBS-QB3, a complete basis set composite energy method. The result shows that the tautomer a (amide oxime) is more stable than the tautomer b (imino hydroxylamine) as is reported in the literature. In addition, our finding shows that, the energy difference between two tautomers is only in about 4-10 kcal/mol but the barrier energy found in traversing each tautomer to another one is in the range of 33-71 kcal/mol. Therefore, it is impossible to convert these two tautomers to each other at room temperature. Additionally, transition state theory is applied to estimate the barrier energy and reaction rate constants of the hydrogen exchange between tautomers in presence of 1-3 molecules of water. The computed activation barrier shows us that the barrier energy of solvent assisted tautomerism is about 9-20 kcal/mol and lower than simple tautomerism and this water-assisted tautomerism is much faster than simple tautomerism, especially with the assisting two molecules of water.