This is a bicentric, prospective, non randomized study. Pediatric and adult patients will be treated.

Rationale: MSC have shown promising effects by reversal of severe therapy-resistant acute GvHD. As a common therapeutic line of action is not shared for steroid resistant GVHD, it is important to establish the toxicity and the feasibility of preparation and infusion of third party MSCs for acute steroid resistant GVHD and acute phases of chronic steroid resistant GVHD.

A total of 10 patients (pediatric and adults) need to be enrolled in the study. Patients who present clinical signs of either acute or chronic steroid resistant GVHD will receive by intravenous infusion at least two fixed doses of mesenchymal stem cells with 5 to 7 days of interval one from the other, derived from HLA unrelated donor different from the HSC donor (third party donor) regardless of the rate of HLA mismatch.

Primary objectives are to establish the feasibility and the toxicity of preparation and infusions of third party MSCs for the treatment of steroid resistant acute and acute phases of chronic grade II-IV GVHD.

Secondary objectives are:

1. To document the efficacy of MSC infusion in steroid resistant acute and acute phases of chronic GVHD grade II-IV.
2. To document the rate of GVHD recurrence in MSCs infused patients.
3. To document relapse of hematological malignancies post MSC infusions in patients undergoing MSCs treatment for steroid refractory GvHD.
4. To document the overall survival of MSC infused patients for steroid refractory GvHD.

Inclusion Criteria:

1. Informed consent.
2. Patients are required to meet the following inclusion criteria:

Any patient that has undergone allogeneic stem cell transplantation with steroid refractory grades II-IV acute GvHD either occurring post transplant, or induced by donor lymphocyte infusions (DLI) or T-cell add back, or chronic steroid refractory GVHD in acute phase. Patients may be receiving local best treatment for steroid refractory GVHD. A positive biopsy for GvHD is not required if clinical signs and symptoms are characteristic for GvHD and other etiologies are excluded. See 6.4 for acute GvHD grading.

1. Steroids have been given, for instance methylprednisolone 2 mg/kg/day, for at least 72h in case of progressive acute GvHD, 5 days in case of stable acute GVHD (grade II to IV) or chronic GvHD in active phase, according to the local policy.
2. Despite this treatment, the patient has unresponsive GvHD after 5 days, or progressive acute GvHD after 72 hours. If single organ acute GvHD grade II from gut or liver, either progression from single organ or addition of one or two more organs. As an example, if the patient has grade II acute GvHD of the skin, GvHD is more intense and more widespread, or GvHD also includes liver and/or gut.
3. Patients with steroid refractory GvHD fulfilling the requirements mentioned in a) - b) may be treated with second line therapy according to the clinical guidelines at each center prior to enrolment in this study.
4. Patients under treatment with best available local treatment for steroid resistant GVHD will not interrupt the ongoing treatment unless clinically required for safety reasons.

Exclusion Criteria:

1. Inability to obtain informed consent.
2. Patients with documented uncontrolled EBV, CMV or fungal infection.
3. Patients in poor clinical conditions with life expectancy of less than 30 days.