Inthispaper,weinvestigatesomedelayGronwalltypeinequalitiesontimescalesbyusingGronwall’sinequality.Ourresultsunifyandextendsomedelayintegralinequalitiesandtheircorrespondingdiscreteanalogues.Theinequalitiesgivenherecanbeusedashandytoolsinthequalitativetheoryofcertainclassesofdelaydynamicequationsontimescales.