Conductivity and photoconductivity properties of individual GaAs/AlGaAs core-shell nanowires (NWs) are reported. The NWs were grown by Au-assisted metalorganic vapor phase epitaxy, and then dispersed on a substrate where electrical contacts were defined on the individual NWs by electron beam induced deposition. Under dark conditions, the carrier transport along the NW is found to be limited by Schottky contacts, and influenced by the presence of an oxide layer. Nonetheless, under illumination, the GaAs/AlGaAs core-shell NW shows a significant photocurrent, much higher than the bare GaAs NW. The spatial dependence of the photocurrent within the single core-shell NW, evaluated by a mapping technique, confirms the blocking behavior of the contacts. Moreover, local spectral measurements were performed which allow one to discriminate the contribution of carriers photogenerated in the core and in the shell.