Oxygen isotope exchange for sodium- and copper-containing mordenite was studied in the isothermal regime using a plug-flow reactor. No prominent exchange was observed over sodium mordenite at 873 K. In contrast, the presence of copper significantly increases the lability of oxygen atoms resulting in a substantial rate of isotope exchange in the temperature range between 793 and 873 K. A novel numerical model accounting for two kinetically distinct sources of exchangeable oxygen atoms was proposed and shown to provide high quality of fitting of experimental data. Two types of exchangeable atoms correspond to about 9 and 25% of the total amount of oxygen atoms, respectively, and these values do not change with the exchange temperature. The exchange mechanism involving two oxygen atoms from the surface dominates in the case of the first source of exchangeable atoms, while the second source undergoes exchange mainly via a single-atom exchange mechanism.