The phonon energies of AlGaP in wurtzite crystal structure are generally not known, as opposed to their zincblende counterparts, because AlGaP crystallizes in zincblende phase in bulk and thin films structures. However, in nanowires AlGaP can be grown in wurtzite crystal structure. In this work we have grown wurtzite GaP/AlGaP/GaP core-shell nanowires by use of MOVPE. After developing suitable growth conditions, the Al composition was determined by STEM-EDX measurements and the wurtzite AlGaP phonon energies by Raman spectroscopy. Raman measurements show a peak shift with increasing Al composition in the AlGaP shell. We find that the phonon energies for wurtzite AlGaP are slightly lower than for zincblende AlGaP. Our results can be used to determine the Al composition in wurtzite AlGaP by Raman scattering.