For certain types of compliant structures, the designer must consider limit states associated with the onset of fluidelastic instability. These limit states may include bifurcations from motion in a safe region of phase space to chaotic motion with exits (jumps) out of the safe region. In practice, such bifurcations occur in systems with noisy or stochastic excitations. For a wide class of dynamical systems, a fundamental connection between deterministic and stochastic chaos allows the application to stochastic systems of a necessary condition for the occurrence of chaos originally obtained by Melnikov for the deterministic case. We discuss the application of this condition to obtain probabilities that chaotic motions with jumps cannot occur in multistable systems excited by processes with tail-limited marginal distributions.