A method is provided for treating individuals suffering from cancer characterized by tumor cells which are telomerase negative, do not have telomerase activity or have L1RT expression or alternative lengthening of telomeres. The method includes administering to an individual in need of treatment thereof, and having the aforementioned cancer, a therapeutically effective amount of a nucleoside analog selected from one or more of the group consisting of: 3′-azido-2′,3′-dideoxythymidine (AZT), 2′,3′-dideoxyinosine (ddI) and 2′,3′-didehydro-3′-deoxythymidine (d4T).
