A variable-displacement rotary fluid compressor comprising first and second rotary compressor assemblies including respective rotor units rotatable about axes aligned with each other and first and second drive shafts respectively carrying and rotatable with the rotor units, each of the compressor assemblies having fluid inlet and outlet ports; a fluid inlet chamber communicating with the fluid inlet ports of the two compressor assemblies and a fluid outlet chamber communicating with the fluid outlet ports of the compressor assemblies; a first clutch assembly comprising a drive member which is rotatable about an axis aligned with the axes of rotation of the rotor units and which is to be driven by a drive source, a driven member rotatable with the first drive shaft and coupling means to couple the drive and driven members together when actuated; and a second clutch assembly comprising a driven member rotatable with the second drive shaft and coupling means to couple the respective driven members of the first and second clutch assemblies together when actuated. The compressor may be incorporated as a refrigerant compressor in an air conditioning system for, for example, automotive use.