One aspect of the invention provides a centrifugal compressor unit (1) comprising a first motor (3), at least one compressor (2) comprising a drive shaft (9) driven by the rotor (12) of the first motor (3) and a set of impellers (5, 6, 7, 8) mounted on the drive shaft (9). The first motor (3) and the compressor (2) are mounted in a gas-tight common housing (26) operated by the compressor unit (1). The rotor (12) of the first motor (3) and the drive shaft (9) are connected by a flexible coupling (24) placed in the housing (26). The compressor unit includes a second motor (4) that is placed in the housing and of which the rotor (13) is connected to the drive shaft (9) by a second flexible coupling (25).