The linear Vlasov theory has shown that the relative flow between alpha particles and protons in the fast solar wind can excite both magnetosonic and oblique Alfven modes and the velocity threshold of the Alfven instability is lower than that of the magnetosonic instability. In this paper, hybrid simulations are performed to investigate the nonlinear evolution of parallel and oblique electromagnetic alpha/proton instabilities in the fast solar wind. The parallel proton plasma beta, defined as ¿$parallel$p = 8πnpkBT$parallel$p/B02, is set equal to 0.15, and the initial average value of the alpha/proton relative flow speed is chosen as 1.76vA (vA is the local Alfven speed). The influences of the temperature anisotropy of alpha particles (T$perp$α/T$parallel$α) and temperature anisotropy of protons (T$perp$p/T$parallel$p) on the alpha/proton instabilities are also considered. The decrease of the temperature anisotropy of alpha particles (T$perp$α/T$parallel$α) can significantly enhance the amplitude of both the magnetosonic and oblique Alfven modes and decelerate alpha particles more efficiently, while the temperature anisotropy of protons (T$perp$p/T$parallel$p) tends to reduce the amplitudes of these two modes. Moreover, in the two-dimensional hybrid simulations the magnetosonic waves are first excited. Then the oblique Alfven waves are also excited and dominate the wave spectrum at the late stage of time evolution. The implications of our simulation results on observations in the fast solar wind are also discussed.