5 Conclusions Acknowledgments References 11 [6] AKHMET, M. U.: Devaney’s chaos of a relay system , Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 1486–1493. [5] AKHMET, M. U.: Li-Yorke chaos in the system with impacts , J. Math. Anal. Appl. 351 (2009), 804–810. [4] AKHMET, M. U.: The complex dynamics of the cardiovascular system , Nonlinear Analysis 71 (2009), e1922–e1931. [3] AKHMET, M. U.: Homoclinical structure of the chaotic attractor , Commun. Nonlinear Sci. Numer. Simulat. 15 (2010), 819–822. [2] AKHMET, M. U.—BEKMUKHAMBETOVA, G.A.: A prototype compartmental model of blood pressure distribution , Nonlinear Analysis: Real World Applications 11 (2010), 1249–1257. [1] AKHMET, M.: Principles of Discontinuous Dynamical Systems , Springer, New York, 2010. This work is supported by the 2219 scholarship programme of TÜBİTAK, the Scientific and Techno- logical Research Council of Turkey. The authors wish to express their sincere gratitude to the referees for the helpful criticism and valuable suggestions, which helped to improve the paper significantly. In this study, we rigorously prove the presence of homoclinic and heteroclinic motions in hybrid systems with impacts. The dynamics of the system under consideration consist of an impulsive differential equation and a discrete map, which influences the former. According to our results, homoclinic and heteroclinic orbits of the discrete map give rise to the emergence of homoclinic and heteroclinic motions in the impulsive system. The presented technique is appropriate to design mechanical and electrical impulsive systems with homoclinic and heteroclinic motions, without any restriction in the dimension. One can take advantage of our approach to investigate the presence of such motions in hybrid systems with impacts. An impulsive Duffing equation is utilized to illustrate the results of the paper. The provided examples show the applicability of our results.