A gasdynamic arrangement for a multi-stage centrifugal turbomachine, such as a two-stage compressor, comprising two coaxial impellers assembled on a common shaft with axial intake ports and radial peripheral discharge zones, the intake ports of the two impellers preferably pointing away from each other; a cylindrical vessel concentrically housing the impellers and the intake duct; a partition wall between the two impellers having a first and a second group of apertures; a first array of curved ducts conveying the flow from the first impeller discharge zone to the first group of apertures in the partition wall, the flow further passing through a chamber in the vessel to the intake port of the second impeller, and a second array of curved ducts conveying the flow from the second impeller discharge zone to the second group of apertures in the partition wall, the flow further going to the discharge port, the two flows bypassing each other in opposing directions at the partition wall.