The secondary system such as pipings, tanks and other mechanical equipment is installed in the primary system such as building. The secondary system has many nonlinear characteristics. The friction or collision characteristic, which is observed in mechanical supports and joints, is the most common nonlinear characteristic. In this paper, estimation method of the first excursion probability of the secondary system with friction or gap, subjected to earthquake excitation is shown. In aseismic design, the maximum response is usually used. Then, the tolerance level is normalized by the maximum response. When the tolerance level is normalized by the maximum response of the secondary system with friction or gap, the first excursion probability does not depend on nonlinear parameters.