A multistage hydraulic system for converting the potential energy of a pressurized gas, particularly air, into mechanical work when rotating a shaft (A.1.1) in one direction, and for producing compressed gas from the mechanical work of the rotating shaft, when rotating the said shaft in the reverse direction or in the same direction, by performing successive quasi-isothermal expansion/compression of the gas, wherein the said system comprises: - A multistage hydraulic gas Compression/Expansion Unit (A.3) made of several Compression/Expansion Modules (A3a-A3d) each having a compression/expansion chamber in which compression and expansion of the gas can take place, the Compression/Expansion Modules (A3a-A3d) each having compression/expansion chambers of different volumes, each compression/expansion chamber being operable alternately in compression or expansion in phase opposition with the bigger/smaller compression/expansion chamber of a consecutive Module, each Module integrating an internal gas/liquid separating heat exchanger (A.3.1.3a - A.3.1.3d) and being arranged to convert pressure power into hydraulic power of an active liquid, and vice-versa, by quasi-isothermal compression/expansion of the gas; - An external Heat Exchanger (A.2) located outside the Compression/Expansion Unit (A.3) for externally circulating active liquid that has been heated/cooled in the Compression/Expansion Unit (A.3) by gas compression/expansion, and arranged to bring the externally circulating active liquid to a substantially constant temperature by heat transfer with ambient air; and - A reversible, multi-circuit multi-displacement Hydraulic Motor/Pump (A.1) having a common driving/driven rotatable shaft, said Hydraulic Motor/Pump being arranged to convert hydraulic power into mechanical power of said rotatable shaft, and vice-versa, the Hydraulic Motor/Pump (A.1) having several circuits in correspondence with the Compression/Expansion Modules (A3a-A3d) of the Compression/Expansion Unit (A.3), each said circuit being of different displacement and being connected to a Compression/Expansion Module (A3a-A3d) of corresponding displacement or volume. - A multistage hydraulic gas Compression/Expansion Unit (A.3) made of several Compression/Expansion Modules (A3a-A3d) each having a compression/expansion chamber in which compression and expansion of the gas can take place, the Compression/Expansion Modules (A3a-A3d) each having compression/expansion chambers of different volumes, each compression/expansion chamber being operable alternately in compression or expansion in phase opposition with the bigger/smaller compression/expansion chamber of a consecutive Module, each Module integrating an internal gas/liquid separating heat exchanger (A.3.1.3a - A.3.1.3d) and being arranged to convert pressure power into hydraulic power of an active liquid, and vice-versa, by quasi-isothermal compression/expansion of the gas; - An external Heat Exchanger (A.2) located outside the Compression/Expansion Unit (A.3) for externally circulating active liquid that has been heated/cooled in the Compression/Expansion Unit (A.3) by gas compression/expansion, and arranged to bring the externally circulating active liquid to a substantially constant temperature by heat transfer with ambient air; and - A reversible, multi-circuit multi-displacement Hydraulic Motor/Pump (A.1) having a common driving/driven rotatable shaft, said Hydraulic Motor/Pump being arranged to convert hydraulic power into mechanical power of said rotatable shaft, and vice-versa, the Hydraulic Motor/Pump (A.1) having several circuits in correspondence with the Compression/Expansion Modules (A3a-A3d) of the Compression/Expansion Unit (A.3), each said circuit being of different displacement and being connected to a Compression/Expansion Module (A3a-A3d) of corresponding displacement or volume.