GaAs, AlGaAs and GaAs-AlGaAs core-shell nanowires (NWs) may find potential applications in the fields of photo-detectors and solar cells. Here we present their self-assembly by Au-catalysed metalorganic vapour phase epitaxy and related physical properties. While AlGaAs NWs show an inherent tapered morphology and unintentional core-shell compositional structure, under selected conditions nearly cylindrical GaAs NWs can be grown; the latter have been used to synthesise straight uniform GaAs-AlGaAs core-shell NWs, showing intense luminescence from both core and shell materials. The dominant GaAs core emission red-shifts with decreasing the precursors V:III ratio, an effect ascribed to the build-up of a space-charge induced electric field at the GaAs-AlGaAs hetero-interface, in turn due to unintentional C and Si doping of GaAs and AlGaAs, respectively.