Acyclic nucleoside analogs such as acyclovir, ganciclovir, penciclovir and the corresponding pro-drugs, i.e., valacyclovir, valganciclovir and famciclovir, respectively have been identified as inhibitors or antagonists of both telomerase (encoded by TERT) and reverse transcriptase encoded by L-1 (LINE-1) RT, and as useful for treating or preventing cancers induced or mediated by the two enzymes. Method of treating or preventing such cancers in patients involves administration of a therapeutically effective amount of a composition having an inhibitor or antagonist of the reverse transcriptases in cells of the patients. The inhibitor or antagonist blocks lengthening of telomeres in telomerase positive and telomerase negative cells. Methods and kits for detecting pathologically proliferating cells expressing TERT and L1RT are also disclosed.