Many researchers caution that extreme observations are becoming more and more frequent in the fields of environment, financial markets, and signal and image processing.Classical time series models are not capable of describing extreme events which are observed over time and exhibit dynamic behaviors.This talk introduces new classes of models, i.e.multivariate msxima of moving maxima processes with sparse random coefficient matrix specification, and max autoregressive processes with log-positive alpha stable noises and hidden max Gumbel shocks.They are closely related but with different focuses.