We report the synthesis and characterization of phase-change Ge-Sb nanowires with two different eutectic compositions and their memory switching characteristics. Under application of electric-fields with controlled pulse amplitude and duration times, Sb-rich (Sb > or = 86 at. %) eutectic Ge-Sb nanowires show phase-change based memory switching, while another eutectic GeSb (Ge:Sb = 1:1) nanowires do not show electronic memory switching at all. However, under repeated measurements, Sb-rich Ge-Sb nanowires display an increase of resistance of the low resistive state. The observed electrical irreversibility for Sb-rich Ge-Sb nanowires is attributed to the structural and compositional instability due to the phase-separation of Ge out of homogeneous Ge-Sb as observed from rapid thermal annealing and transmission electron microscopy experiments. Implications for design of Te-free nanoscale materials for phase change memory applications are also discussed.