Adaptive identification of rapidly changing parameters is essentially needed in adaptive signal processing and adaptive control. New accelerated LMS and RLS type of adaptive algorithms are given from a standpoint that any parameter changes can be approximately expressed by a finite degree of polynomial function of time. The proposed adaptive algorithm involves ordinary LMS and RLS algorithms as special cases, which are based on the assumption that the parameters are constant but unknown. A sufficient condition for assuring stability of the accelerated adaptive algorithm is clarified based on the small gain and passivity theorems. The effectiveness is examined in numerical simulations-and experiments in which adaptive equalization for fading channel and adaptive direction-of-arrival tracking experiments.