The nucleation rate depends on the free-energy barrier and the kinetic factor. While the role of the free energy barrier is a text-book subject, the importance of the kinetic factor is frequently underestimated. In this study, we applied the mean first-passage time method, to obtain the free-energy landscape and kinetic factor directly from the molecular dynamics (MD) simulations of the nucleation of the face-centered cubic (fcc) phase in the pure Ni and the B2 phases in the N i 50 A l 50 and C u 50 Z r 50 alloys. The obtained data show that while the free-energy barrier for nucleation is higher in pure Ni the nucleation rate is considerably lower in the N i 50 A l 50 alloy. This result can be explained by the slow attachment kinetics in the N i 50 A l 50 alloy, which was related to the ordered nature of the B2 phase. Even smaller fraction of the antisite defects in the C u 50 Z r 50 alloy leads to such a slow attachment kinetics that the nucleation is never observed for this alloy in the course of the MD simulation. This is consistent with the experimental facts that the C u 50 Z r 50 alloy is a good glass forming alloy and the N i 50 A l 50 alloy is not. Thus the present study demonstrates that the atom attachment rate can be the critical factor that controls the nucleation process under certain conditions.