Abstract: The possibility in principle of the MBE (molecular-beam epitaxy) growth of GaP and InP nanowires on a SiC substrate with a graphene layer is demonstrated for the first time. InP nanowires on such a substrate have no stacking faults and possess an ideal crystallographic quality. At the same time, GaP nanowires have structural defects of the type of twins and the reversal of crystallographic phases at the top and at the base. The results of structural measurements demonstrate that the nanowires are formed in the wurtzite phase, which is not typical of bulk III–V materials.