OUTLINE: This is a randomized study. Patients are stratified according to the type of bone marrow transplant received (allogeneic vs matched unrelated donor) and type of chronic graft vs host disease (steroid dependent vs steroid refractory). Patients receive either oral thalidomide or placebo 2-4 times a day for 6 months. The drug is then tapered until stopped. If disease recurs, the drug may be restarted for a second 6 month course. The maximum duration of treatment is 18 months. Patients continue on steroid therapy, which is tapered during study therapy. If no response is seen after 8 weeks, patients may cross over to the other alternate drug. Patients are followed weekly for 1 month, then every month for 1 year.