An integrated high-pressure compression unit for a process fluid that includes at least a first compression device able to compress the process fluid from a essentially gaseous initial thermodynamic state to an intermediate thermodynamic state, a second compression device connected mechanically to the first compression device and able to compress the process fluid from the intermediate thermodynamic state to a final thermodynamic state, a motor device able to drive the first compression device and the second compression device, and a pressure casing or housing in which at least the said first and second compression devices are mechanically coupled to each other.