To prevent the resistance to Glivec in patients with chronic myelogenous leukaemia (CML), it is necessary to get a good understanding of its potential mechanisms. The present hypothesis accents on the mechanisms whereby Bcr-Abl tyrosine kinase remains inhibited by Glivec, but alternative signalling pathways become activated-the potential reason associates with activation of telomerase after long-term treatment with Glivec and recovery of cell proliferation and immortality. The hypothesis is based on the observations about differences in telomere dynamics and telomerase activity between chronic and blast phases of CML patients, as well as about the potential effect of Glivec on the cross-talk between telomerase, Bcr-Abl tyrosine kinase and protein kinase C family-key enzymes in CML. It proceeds from recently published data, demonstrating that protein kinase C activates and c-Abl tyrosine kinase inhibits telomerase. During optimization of chemical structure, Glivec loose its effect on protein kinase C and enhances the effect on Bcr-Abl tyrosine kinase, resulting in a high potential to activate telomerase indirectly through its effect on both kinases. Experimental preclinical data are given in confirmation of this hypothesis.