A closed circuit hydrostatic system comprising a single-rod hydraulic actuator having a cylinder (1.3), a piston (1.1), a piston- rod (1.2), a cap-side chamber (1.4) and a rod-side chamber (1.5); a flow rate controlled pump having two ports and which can generate flow in two directions; a hydraulic accumulator and a 3-way, 3-positions internal pilot fluid operated shuttle valve, the cap-side chamber (1.4) of the single-rod hydraulic actuator having a port directly connected to one of the ports of the pump through a cap-side chamber fluid line, the rod-side chamber (1.5) of the single-rod hydraulic actuator having a port directly connected to the other port of the pump through a rod-side chamber fluid line, the flow rate controlled pump regulating the flow rate going to said single-rod hydraulic actuator, the hydraulic accumulator being used for compensating the differential flow rate formed in the closed circuit due to hydraulic actuator movement, and the shuttle valve providing bidirectional flow between the closed circuit and said hydraulic accumulator and comprising a body (4.1), a shuttle valve spool (4.2) which is connected to a valve centering spring (4.3) from its one end, at the inner part of the body (4.1), the shuttle valve further comprising: • port A (4.4) fluidly connected to the cap-side chamber (1.4) through the cap-side chamber fluid line and the port of the cap-side chamber (1.4) found on the cylinder (1.3) of the hydraulic actuator, • port B (4.5) fluidly connected to the rod-side chamber (1.5) through the rod-side chamber fluid line and the port of the rod-side chamber (1.5) found on the cylinder (1.3) of the hydraulic actuator, and • port C (4.6) fluidly connected to the hydraulic accumulator through a hydraulic accumulator fluid line which are found on said 3-way, 3-position internal pilot operated shuttle valve body (4.1) and, characterized in that, with the operation of the closed circuit hydrostatic system in order to prevent the instability problem encountered during compensation of the differential flow rate occurring as a result of the asymmetric hydraulic actuator structure, • a valve spool overlap (4.7) found between Port A (4.4) that is connected to the cap-side chamber (1.4) of the hydraulic actuator and Port C (4.6) that is connected to the hydraulic accumulator; and preventing the flow between the hydraulic accumulator line connected to said hydraulic accumulator and the cap-side chamber line connected to the cap-side chamber (1.4) of the hydraulic actuator, and • a valve spool underlap (4.8) found between Port B (4.5) that is connected to the rod-side chamber (1.5) of the hydraulic actuator and Port C (4.6) that is connected to the hydraulic accumulator; and enabling flow between the hydraulic accumulator line connected to the hydraulic accumulator and the rod-side chamber line connected to the rod-side chamber (1.5) of the hydraulic actuator which are formed on the shuttle valve spool (4.2) in the central position of the shuttle valve, that results in closed and partially open orifice forms between A-C and B-C conduits respectively. • port A (4.4) fluidly connected to the cap-side chamber (1.4) through the cap-side chamber fluid line and the port of the cap-side chamber (1.4) found on the cylinder (1.3) of the hydraulic actuator, • port B (4.5) fluidly connected to the rod-side chamber (1.5) through the rod-side chamber fluid line and the port of the rod-side chamber (1.5) found on the cylinder (1.3) of the hydraulic actuator, and • port C (4.6) fluidly connected to the hydraulic accumulator through a hydraulic accumulator fluid line • a valve spool overlap (4.7) found between Port A (4.4) that is connected to the cap-side chamber (1.4) of the hydraulic actuator and Port C (4.6) that is connected to the hydraulic accumulator; and preventing the flow between the hydraulic accumulator line connected to said hydraulic accumulator and the cap-side chamber line connected to the cap-side chamber (1.4) of the hydraulic actuator, and • a valve spool underlap (4.8) found between Port B (4.5) that is connected to the rod-side chamber (1.5) of the hydraulic actuator and Port C (4.6) that is connected to the hydraulic accumulator; and enabling flow between the hydraulic accumulator line connected to the hydraulic accumulator and the rod-side chamber line connected to the rod-side chamber (1.5) of the hydraulic actuator