Severe polymyositis or dermatomyositis which responds poorly to corticosteroids may be difficult to treat. Because of anecdotal reports suggesting efficacy, we are comparing plasmapheresis and leukapheresis with a sham procedure. Patients who fail to respond will be offered pulse intravenous cyclophosphamide. Starting in the summer of 1987, patients who qualify will be randomized to receive either intravenous methotrexate with leukovorin rescue or a combination of methotrexate and azathioprine.