The present invention concerns a method of treating chronic myelogenous leukemia, a related myeloproliferative disorder or a Ph-positive acute lymphocytic leukemia in a subject animal, comprising:

• (a) selecting or identifying an animal suffering from chronic myelogenous leukemia or a related myeloproliferative disorder and showing resistance or intolerance to treatment with STI571; and
• (b) administering to the animal homoharringtonine.

In a preferred embodiment, the animal is a human being.