Multistage hydraulic systems and methods for converting the potential energy of a pressurized gas, particularly air, into mechanical work operating in motor, and for producing compressed gas from the mechanical work of the rotating shaft (A1.1 ) when rotating when operating in compressor mode, by performing a successive expansion / compression of the said gas. Each of the systems comprises: a multistage Compression-Expansion Unit (1.3) made of several hydraulic Compression-Expansion Modules (A.3a to A.3d) having different capacity and integrating a gas / liquid separating heat exchanger (A.3.1.5) designed to convert pressure power into a hydraulic power and vice-versa, by performing an essentially isothermal compression / expansion of the gas, a single stage or multistage, direct or indirect, external forced-air Heat Exchanger (A.2) for maintaining the active liquid at ambient temperature and a multi-circuit, multi-displacement Hydraulic Motor / Pump (A.1) for converting hydraulic power into mechanical power and vice-versa.