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The magnetic properties and phase transition kinetics during antiferromagnetic (AFM) to ferromagnetic (FM) phase transition in epitaxial-grown Fe50(Rh1-XPtX)50 thin films were investigated in the present study. X-ray diffraction results show a change of ~0.6% in c lattice parameter during AFM to FM phase transition in Fe50(Rh0.95Pt0.05)50 thin film. The substitution of Pt is very effective not only for tuning the first-order AFM/FM phase transition behavior but also for decreasing the thermal hysteresis. The time dependent magnetization measurement indicates that the clusters of the FM phase nucleate in the AFM matrix heterogeneously and vice versa during the first-order phase transition in ordered FeRh-Pt thin films. The nucleation and growth kinetics of the first-order phase transition in Fe50(Rh1-XPtX)50 thin films was described by the classical Kolmogorov-Johnson-Mehl-Avrami model.