The trajectory bounds of simple and large-scale interconnected discontinuous systems are treated within a stability framework. In doing so, stability is defined in terms ofpre-specifiedsubsets of the state space over an infinite time interval (practical stability) and over a finite time interval (finite time stability). The discontinuous systems considered are those which are described by ordinary discontinuous differential equations which may be autonomous or non-autonomous, linear or non-linear, unforced or under the influence of persistent disturbances, simple or interconnected. In all cases it is assumed that the differential equation possesses solutions in the sense of Filippov.