Despite good progress during the last decade, hemophagocytic lymphohistiocytosis (HLH) remains difficult to treat. Two different treatment regimens have been used successfully. The first one, a treatment regimen based on two drugs called etoposide and dexamethasone, has been used worldwide. The second regimen, based on two drugs called Anti-thymocyte globulin (ATG) and prednisone, has been used mostly at one hospital in Paris, for over 15 years. With either regimen, about three quarters of treated children survive the most difficult time, the first two months after diagnosis. These two different regimens appear to work somewhat differently, and we suspect that combining them may give better results than either regimen alone. We are conducting this clinical trial to test the combination of ATG, dexamethasone, and etoposide for the treatment of HLH. The purpose of this research study is to find out what effects (good and bad) this drug combination has on you and your HLH.