The theory of late-stage evolution of island films from the eutectic composition binary melt is developed. The complete system of equations describing the island film evolution on the substrate surface at the stage of Ostwald ripening is suggested. The asymptotic solution of that system of equations reveals a strong correlation in the evolution of the islands of different compositions at the Ostwald ripening stage which is associated with some specific features of eutectic systems. All main characteristics of island films at the late evolution stage such as islands size distribution function, critical sizes and density of the islands have been obtained. Relations between the individual agents constants causing predisposition of the eutectic system to one of the specific mechanisms of heat mass transfer have been found. The processes accompanying growth of the films from the eutectic composition melts in the presence of heat sink are discussed.