The dynamical model of a twodegreeoffreedom vibroimpact system with two motion limiting constraints was established, whose sticking conditions were given. The analysis shows that there exist sticking motions. According to the shooting method, the unstable periodic motion of vibroimpact, i.e. the fixed point of Poincaré section, was solved by the method of varied step and gradual iteration. Hopf bifurcation and perioddoubling bifurcation were analyzed under certain parameters by numerical simulation. At the same time the quasiperiodic responses of the system represented by invariant circles in the projected Poincaré section of twodegreeoffreedom system with two motion limiting constraints were obtained by numerical simulations. As the controlling parameter varied further, the routes of the twodegreeoffreedom system with two motion limiting constraints to chaos via quasiperiod bifurcation and perioddoubling bifurcation were investigated respectively.