The present invention relates to a method of treating cancers, especially those showing resistance to classical anti-pro liferative chemotherapy drugs. Further, the invention provides a specific interferon alpha sequential regimen for treating cancers, especially those showing resistance to classical anti-proliferative chemotherapy drugs such as stem cell driven cancers. More specifically, the invention relates to a use of IFN alpha for the preparation of a pharmaceutical formulation for the treatment of cancers wherein the pharmaceutical formulation is to be administered following a sequential administration pattern i.e. an induction period wherein a therapeutically effective amount of IFN alpha is administered, a period during which ni IFN alpha is administrated and a chemotherapy period wherein a therapeutically effective amount of a chemotherapeutic agent is administered.