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This new approach provides a unified and consistent framework for introducing time\u2010varying parameters in a wide class of nonlinear models. The GAS model encompasses other well\u2010known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time\u2010varying mean. In addition, our approach can lead to new formulations of observation\u2010driven models. We illustrate our framework by introducing new model specifications for time\u2010varying copula functions and for multivariate point processes with time\u2010varying parameters. We study the models in detail and provide simulation and empirical evidence. 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