The integrally geared compressor comprises a bull gear supported for rotation in a gear casing, and a plurality of pinion shafts supported for rotation in the gear casing. Each pinion shaft comprises a respective pinion, which meshes with the bull gear. A first pinion shaft has a first end drivingly coupled to an axial compressor unit comprising a gas inlet, a gas outlet and an axial compression wheel. A second pinion shaft is drivingly coupled to a centrifugal compressor arrangement.