 The allogeneic stem cell transplantation is a successful therapeutic approach in the treatment of a number of hematologic diseases. Nevertheless, it is associated with substantial risks and complications. A major life-threatening complication that occurs in the post transplantation period is the graft versus host disease, especially its severe forms Grade III and Grade IV. For this reason, a combined immunosuppressive therapy is standard in patients after a stem cell transplantation. In this regard, the combination between cyclosporin A and methotrexate in the prevention of GvHD has been particularly successful. However, the incidence rate of GvHD and consequent mortality are still fairly high. Besides, the therapy itself is accompanied by serious side effects. Therefore, there is a need for a more efficient, less toxic, combined immunosuppressive therapy. The purpose of this pilot study is to test a new combination of immunosuppressives tacrolimus and everolimus for the prevention of GvHD after an allogeneic stem cell transplantation. Tacrolimus is a macrolide immunosuppressant that acts as a calcineurin inhibitor, thereby preventing the activation and proliferation of the T-lymphocytes. Everolimus is a semisynthetic macrocyclic lactone that inhibits the activity of a key protein involved in the regulation of the cell cycle, the so called m-TOR protein. Both medicaments act complementary and potently inhibit the proliferation of immune cells. Previous studies have shown that the combination of tacrolimus with everolimus decreases significantly the rejection rate after solid organ transplantation and this combination is generally well tolerated. 