 The study drug, BAY59-7939, is a new drug currently being tested in the prevention of VTE. It directly inhibits factor Xa, a blood component in the pathway which leads to coagulation clotting of blood cells. It is available as a tablet. The purpose of this study is to compare the safety and efficacy of BAY59-7939 with the safety and efficacy of the licensed drug Enoxaparin. Enoxaparin, a so-called low molecular heparin, is approved and widely used in the area of thromboprophylaxis and will be given once daily subcutaneously. In this study 4 different doses of the investigational drug BAY59-7939 will be tested in comparison to Enoxaparin. You will receive during the study either one of the following BAY59-7939 treatments or Enoxaparin. The following doses of BAY59-7939 will be tested: Dose I ; Dose II, Dose III, Dose IV. This study will run for approximately 7 months in a number of countries. In total, up to 600 patients may participate in this study. 