A proton/alpha magnetosonic instability is investigated in the framework of the linear theory of plasma waves for conditions typical of the fast solar wind. Warm streaming alpha particles with a differential speed, the speed relative to the major ions/protons, v&agr;, close to the Alfv¿n speed, are found to significantly enhance a magnetosonic instability when their temperature anisotropy &Ggr;i=Ti⊥/Ti∥ is less than 1. Here Ti∥ and Ti⊥ denote the velocity distribution parallel and perpendicular to the magnetic field. The possible role of the instability in limiting the relative speed between alpha particles and protons in the fast solar wind is discussed. ¿ 2000 American Geophysical Union