A fluid flow machine, particularly a centrifugal pump, wherein the casing has a tubular first portion serving to convey a stream of fluid radially toward a pump shaft which drives one or more impellers. The casing has a second portion with an arcuate band-like wall which spacedly surrounds the shaft and defines a passage having an oval cross-sectional outline and receiving fluid from the outlet of the first portion. A cylindrical outlet of the passage is adjacent the foremost impeller or the only impeller of the pump. One or more guides are provided in the passage to control the flow of fluid from the outlet of the first portion of the casing toward and into the range of the foremost impeller.
