An electro-hydrostatic actuation system and a method for driving a hydraulic actuator, e.g. a hydraulic cylinder, are described, wherein the system comprising a leakage branch, and wherein preferably an additional pump is arranged. The system further comprises a source for providing hydraulic liquid; a high-pressure circuit to direct the hydraulic liquid to a hydraulic actuator, such as e.g. a hydraulic cylinder; a low-pressure circuit having several branches; a main pump for hydraulic liquid arranged in the high-pressure circuit, comprising a housing having a high-pressure section and a low-pressure section, separated by gap sealings, wherein the high-pressure section comprises a first outlet and a second outlet to provide the hydraulic liquid flow in the high-pressure circuit; and wherein the low- pressure section comprises a leakage outlet; an electric motor driving the main pump.