Described are methods for treating hyperproliferative disorders, including cancers, by administering to the affected mammal (e.g., human) an effective amount of a composition comprising one or more oligonucleotides which share at least 33% but less than 100% nucleotide sequence identity with the human telomere overhang repeat. Methods of treatment or prevention of hyperproliferative diseases or pre-cancerous conditions affecting epithelial cells, such as psoriasis, atopic dermatitis, or hyperprolferative diseases of other epithelia and methods for reducing photoaging, or oxidative stress or for prophylaxis against or reduction in the likelihood of the development of skin cancer, are also disclosed. The compositions and methods are also useful to treating other cancers.