The detection of nonbaryonic dark matter through its gamma-ray annihilation in the center of our galaxy has been studied. The gamma fluxes according to different models have been simulated and compared to those expected to be observed with the Alpha Magnetic Spectrometer (AMS), during a long-term mission on board of the international space station. Under the assumption that the dark matter is composed of the lightest, stable supersymmetric particle, the neutralino, the results of the simulations in the framework of minimal supergravity models, show that with a cuspy dark matter halo profile or a clumpy halo, the annihilation gamma-ray signal would be detected by AMS. More optimistic perspectives are obtained with the anomaly mediated supersymmetry breaking (AMSB) model. The latter leads also to a cosmologically important Li2 abundance. Finally, the discovery potential for the massive Kaluza-Klein dark matter candidates has been evaluated and their detection looks feasible.