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Terahertz (THz) emission from GaAs-AlGaAs core-shell nanowires (CSNW) on silicon (100) substrates was investigated using THz time-domain spectroscopy. The applied magnetic field polarity dependence strongly suggests that THz emission originated from photo-carriers in the CSNWs. Optical excitation of the GaAs-AlGaAs core-shell yielded a wider THz emission bandwidth compared with that of just the GaAs core material. This result is currently attributed to faster carrier lifetimes in the AlGaAs shell. The THz emission spectral data are supported by time-resolved photoluminescence studies.