A Phase I/II, open-label, dose-escalation pilot study designed to obtain preliminary safety, pharmacokinetic (PK) and efficacy information on visilizumab administered as a first-line therapy to patients with acute, Grade II, III, or IV graft-versus-host disease (GVHD). It is anticipated that up to 34 patients at up to 10 study centers could be eligible for enrollment in this study. Patients will be eligible for enrollment within 24 hours of beginning standard steroid treatment (2 mg/kg of methylprednisolone IV, or 10 mg/kg hydrocortisone IV, per day). Steroids will be rapidly tapered over one week following visilizumab administration.