The global properties of a two-degree-of-freedom impact system under certain parame-ters were studied in the thesis.This research discovered the phenomenon of coexistence of attractors.Predicated on the cell-mapping theory, further researches on this phenomenon were conducted withthe method of step-changing technique.The results worked out the periodic solutions in certain in-terval analysis, as well as its attraction basin on the poincare cross section, verifying the effectivenessof the application of cell-mapping theory in this twovide theoriesKey words:for optimum design of impact system of-degree-of-freedom impact system, and pro-mechanics.