This study is to test the concept that using ECP treatment prior to and after an allogeneic bone marrow transplant (BMT) or peripheral blood stem cell (PBSC) transplant will prevent the development of GvHD. This study is not designed to detect a specific treatment effect. However, some statements about the outcome of the study are possible. A sample size of n = 21 patients could detect a statistically significant difference between the expected rate of GvHD in an untreated population, 60%, and our hypothesized rate, 30%, for the matched-unrelated recipients. This calculation is based on a one-sample, two-sided chi-square test at the 5% level of significance with 80% power.