Inthispaper,theasymptoticbehaviorofthreetypesofpopulationmodelswithdelaysanddiffusionisstudied.ThefirstrepresentsonespeciesgrowthinthepatchΩandperiodicenvironmentandwithdelaysrecruitment,thesecondmodelsasinglespeciesdispersalamongthempatchesofaheterogeneousenvironment,andthethirdmodelsthespreadofbacterialinfections.Sufficientconditionsfortheglobalattractivityofperiodicsolutionareobtainedbythemethodofmonotonetheoryandstronglyconcaveoperators.Someearlierresultsareextendedtopopulationmodelswithdelaysanddiffusion.