Investigations on the dissociation kinetics of hydrated protonium ions, (H(2)O)(2)H(+) and their deuterated species (D(2)O)(2)D(+), are reported based on the harmonic and anharmonic oscillator model using the transition state theory and ab initio calculations. We find that the dissociation of (H(2)O)(2)H(+) and (D(2)O)(2)D(+) exhibits a distinct threshold behavior due to the existence of activation energies. Moreover, the deviation between the harmonic and anharmonic dissociation rate constants becomes larger in the high energy or temperature range, with the rate constants becoming unreasonably large under the harmonic oscillator model. The isotope effect is found to become more distinct but only in the case of the anharmonic oscillator model. These results show that the anharmonic Rice-Ramsperger-Kassel-Marcus (RRKM) theory can provide a reasonably good description for the dissociation of (H(2)O)(2)H(+) and (D(2)O)(2)D(+). Furthermore, a theoretical model to demonstrate the principle of vibrational predissociation spectroscopy (VPS) is established from the viewpoint of RRKM theory and applied in determining the experimental conditions and understanding the role of the dissociation rate constant k(E) played in the VPS experiment, using (H(2)O)(2)H(+) and (D(2)O)(2)D(+) as examples.