So far there were few studies to discuss the long-time tails of autocorrelation functions, but some recent papers indicate roles of long-time tails in granular fluids. If there are the tails, the conventional constitutive equation should be changed. In this talk, we demonstrate the existence of the long-time tails in velocity autocorrelation functions and the shear stress autocorrelation functions, while it is absent in the heat flux autocorrelation function. These results are consistently obtained from the theory and the simulation. The study is based on the collaborative work with Dr. Michio Otsuki[1]. [1] H. Hayakawa and M. Otsuki, arXiv:0706.3956