Abstract: In this paper, by using the theories of Kurzweil integral and bounded $\Phi$-variation function. Emphatic convergence for Kurzweil equations and its application for a sequence of ordinary differential equations are discussed. The theorem of emphatic convergence for bounded $\Phi$-variation solutions of Kurzweil equations is obtained. The result is continuation of continuous dependence of bounded $\Phi$-variation solutions on parameters for Kurzweil equations and essential generalization of the emphatic convergence for bounded variation solutions of Kurzweil equations.

Key words: Kurzweil equations, emphatic convergence, bounded $\Phi$-variation function