Uniform asymptotic stability for general nonlinear time-varying systems is investigated from the output-to-state viewpoint. A unified criterion is proposed using a modified detectability condition and certain integral inequalities. The criterion extends the Krasovskii-LaSalle theorem to nonperiodic time-varying systems. An example taken from the tracking control of mobile robots is given to illustrate that, much as the invariance principle of LaSalle is used in studying the stability of time-invariant systems, our results can be used to study the stability of nonperiodic time-varying systems by checking the modified delectability condition.