Activated diffusion of water between macromolecules in swollen cellulose is accompanied by anomalously high kinetic isotope effects of oxygen. The separation factor of heavy-oxygen water (H 2 18 O /H 2 16 O) is thousands of permilles instead of tens of permilles according to modern Absolute Rate Theory. This anomalous separation under usual conditions is disguised by the opposing process of very fast equalization to equilibrium through water-filled cellulose pores. This process is quicker by approximately 3 orders of magnitude than diffusion through the cellulose body. As a consequence, this opposition-directed equalization virtually eliminates the results of isotope separation. To reveal this anomaly it is necessary to suppress equalization, which was the primary problem for both discovery of this anomaly and its investigation. The method of investigating the anomalous separation in cellulose was developed with suppression of this negative influence. Discussion of the theoretical nature of the anomalous kinetic isotope effect is presented. This theoretical study would probably permit the discovery and use for isotope separation of the anomalously high isotope effect for other chemical elements, in particular, for those heavier than oxygen.