This paper reports on the epitaxial growth of single-crystalline ternary Zn(1-x)Mg(x)Te nanowires covering a broad compositional range of molar fraction 0≤x≤0.75. The nanowires were grown on (100), (110), and (111) GaAs substrates using a vapor-liquid-solid mechanism. Solid source molecular beam epitaxy and an Au-based nanocatalyst were used for these purposes. The composition of nanowires can be adjusted by changing the ratio of Mg to Zn molecular beam fluxes. Electron microscopy images show that the nanowires are smooth and slightly tapered. The diameters of the obtained nanowires are from 30 to 70 nm and their length is around 1 µm. X-ray diffraction analysis and transmission electron microscopy reveal that the nanowires have a zinc-blende structure throughout the whole range of obtained compositions, and have a [Formula: see text] growth axis. The Raman measurements reveal both the expected splitting and shift of phonon lines with increasing Mg content, thus proving the substitutional incorporation of Mg into metallic sites of the ZnTe lattice.