Abstract: In the earlier stage of dispersion process,the rate of dispersion aSsociatedwith earlier discharge is relatively large because the memory term extends further back intime。 In order to investigate the early properties of two-dimensional dispersion,we proposethe delay-diffusion equation as following:which is based on the ansatz derived by Smith(198 1).The analytical expressions forD_(xx):,D_(yx),D_(xy) ,D_(yy) and,are obtained.