A hydrostatic drive has a hydrostatic pump (3) driven by a drive motor (2) and connected in a closed circuit with a hydrostatic motor (4). The closed circuit is formed by a first hydraulic connection (6a) and a second hydraulic connection (6b). Each of the hydraulic connections (6a, 6b) can form the high-pressure side or the low-pressure side of the closed circuit. A high pressure accumulator device (20) can be connected with the respective high-pressure side hydraulic connection (6a, 6b) and, simultaneously, the respective low-pressure side hydraulic connection (6b, 6a) can be connected with a hydraulic balancing device (30). A valve device (50) is provided for this simultaneous connection. The valve device (50) is a hydraulically controlled shuttle valve device (51) connected to the two hydraulic connections (6a, 6b), the high pressure accumulator device (20) and the hydraulic balancing device (30). The shuttle valve device (30) has a high pressure accumulator path (51a) and a hydraulic balancing path (51b), and is in communication with the two hydraulic connections (6a, 6b) of the closed circuit.