Thispaperisconcernedwiththeglobalexistenceanduniformboundednessofsolutionsfortwoclassesofchemotaxismodelsintwoorthreedimensionalspaces.Firstly,byusingdetailedenergyestimates,specialinterpolationrelationanduniformGronwallinequality,weprovetheglobalexistenceofuniformlyboundedsolutionsforaclassofchemotacticsystemswithlinearchemotactic-sensitivitytermsandlogisticreactionterms.Secondly,byapplyingdetailedanalyticsemigroupestimatesandspecialiterationtechniques,weobtaintheglobalexistenceofuniformlyboundedsolutionsforaclassofchemotacticsystemswithnonlinearchemotacticsensitivityterms,whichextendstheglobalexistenceresultsof[6]toothergeneralcases.