We announce new methods for explicitly constructing strict input-to-state stable (ISS) Lyapunov functions for time-varying nonlinear systems. Our constructions are expressed in terms of nonstrict ISS Lyapunov functions which we assume are given. The nonstrict Lyapunov functions can in turn he constructed by known methods for many systems of interest. We also provide a new method for explicitly constructing input-to-output stable (IOS) Lyapunov functions for time-varying systems with outputs. We illustrate our results using a tracking problem for a rotating rigid body.