This compressor unit comprises a motor (34) and at least one compressor (44) comprising a driven shaft (54) driven by the rotor of the motor and bladed wheels fitted on the driven shaft (54), the assembly composed of the motor and the compressor being installed in a common casing (55) leak tight to the gas manipulated by the compressor unit. The rotor and the driven shaft are connected through a flexible coupling (72) placed in the casing.