Numerical methods are developed for characterizing extreme responses of dynamical systems to colored and white random inputs. System responses are solutions of stochastic differential equations (SDEs), i.e., deterministic differential equations with random inputs and/or initial conditions. The system FD responses are solutions of these equations to inputs described by the FD models constructed in the previous chapter. Conditions are established under which the distributions of extremes of system responses can be approximated by the distributions of corresponding FD responses. The conditions are essential since most of the stochastic problems have to be solved numerically, numerical methods can only solve finite dimensional problems, i.e., problems involving finite sets of random variables, and continuous-time processes are uncountable families of random variables.