Patients undergoing surgery, especially hip and knee surgery, are at high risk for VTE (up to 60 % without prophylaxis). The administration of drugs for thromboprophylaxis, such as heparins, significantly lowers that risk, but heparins have to be applied below the skin (subcutaneously). Additionally, there is a chance of developing a heparin-induced thrombocytopenia (decrease in platelets). Therefore, there is still a need for new agents which are safer and more efficient and which are easier to apply.The purpose of this study is to compare the safety and efficacy of BAY 59-7939 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.Another important purpose of the study is to find the optimal dose of BAY 59-7939 for thromboprophylaxis after hip replacement surgery. Therefore, there are several dose steps planned.