Abstract: In the present paper,the nonautonomous two-species Predator-Prey models with diffusion are considered. Prey species can diffuse between two patches, while the predator species is confined to one patch and cannot diffuse. It is proved that if the coefficients satisfy certain inequalities,then the system can be made persistent and have a strictly positive periodic orbit which is glotally asymptotically stable.

Key words: Persistence, uniqueness of periodic orbit, global asymptotic stability