Inclusion Criteria: Entry criteria include both of the following: 1.1 Clinical diagnosis of VOD, defined by jaundice (bilirubin ≥2 mg/dL) and at least 2 of the following clinical findings, by Day +35 post stem cell transplant: - Ascites - Weight gain of >/= 5% compared to the day of conditioning-- if this value is not available, the weight on the date of admission to the SCT unit may be used) - Hepatomegaly; increased over baseline (at the time of admission for SCT). Patients that do not meet the criteria in Section 1.1 (i.e. have two of the major criteria but not three) and have biopsy proven VOD are eligible in the presence of characteristics consistent with severe disease (see below) 1.2 Severe VOD, defined as VOD with multi-organ failure (MOF), i.e., presence of one or both of the following, by Day +45 post stem cell transplant: - Renal dysfunction: - Serum creatinine > 3x value on the date of admission to the SCT unit for conditioning or > 3x lowest value during conditioning prior to SCT (whichever is lowest) or - Creatinine clearance or GFR </= 40% of admission value, or - Dialysis dependence; OR - Pulmonary dysfunction: - Documentation of oxygen saturation </= 90% on room air (two consecutive measurements at least one hour apart) or - Requirement for oxygen supplementation /ventilator dependence. Dysfunction must be attributable to fluid overload or mechanical impingement from abdominal distention or hepatic enlargement and not to an infectious cause (e.g., documented pneumonia). - Patient must also provide written informed consent. Exclusion Criteria: - Use of any medication which increases the risk of hemorrhage is disallowed. Use of heparin or other anticoagulants is disallowed within 12 hours unless being used for routine central venous line management, fibrinolytic instillation for central venous line occlusion, intermittent dialysis or ultrafiltration of CVVH. - Clinically significant uncontrolled acute bleeding, defined as hemorrhage requiring > 15 cc/kg of packed red blood cells (e.g., a pediatric patient weighing 20 kg and requiring > 300cc of packed red blood cells/24 hours, or an adult patient weighing 70 kg and requiring >3 units of packed red blood cells/24 hours) to replace blood loss, OR bleeding from a site which in the Investigator's opinion constitutes a potential life-threatening source (e.g. pulmonary hemorrhage or CNS bleeding), irrespective of amount of blood loss, at any point from the date of SCT through the date of severe VOD diagnosis. - Hemodynamic instability as defined by a requirement for multiple pressors, or inability to maintain mean arterial pressure (for children: to maintain mean arterial pressure within 1 standard deviation of age-adjusted levels) with single pressor support. - NB: for sites that have been activated in Protocol Defibrotide 2005-01, patients eligible for this Treatment IND protocol must meet a diagnosis of VOD After Day + 21 from SCT before Day + 3. In addition patients must meet diagnosis of MOF AFTER Day + 28 and BEFORE Day + 4. Patients who meet these criteria Before Day + 21 and Day +28, respectively, must be enrolled in Protocol 2005-01.