A new numerical procedure for efficient dynamics simulations of linear-elastic systems with unilateral contacts is proposed. The method is based on the event-driven integration of a contact problem with a combination of single- and set-valued force laws together with classical model-reduction techniques. According to the contact state, the developed event-driven integration enables the formulation of reduced system matrices. Moreover, to enable the transition among different reduced spaces the formulation of the initial conditions is also presented. The method has been developed separately for each of the four most popular model-reduction techniques (Craig-Bampton, MacNeal, Rubin and Dual Craig-Bampton). The applicability of the newly presented method is demonstrated on a simple clamped-beam structure with a unilateral contact, which is excited with a harmonic force at the free end.