Thispaperdealswiththevectorcontrol,includingboththedirectvectorcontrol(DVC)andtheindirectvectorcontrol(IdVC),ofinductionmotors.ItiswellknownthattheestimationofrotorfluxplaysafundamentalroleintheDVCandtheestimationofrotorresistanceisvitalintheslipcompensationoftheIdVC.Intheseestimations,theprecisionissignificantlyaffectedbythemotorresistances.Therefore,onlineestimationofmotorresistancesisindispensableinpractice.Forafastestimationofmotorresistances,itisnecessarytoslowdowntheconvergencerateofthecurrentestimate.Ontheotherhand,forafastestimationoftherotorflux,itisnecessarytospeedupitsconvergencerate.Itisverydifficulttorealizesuchatrade-offinconvergenceratesinafullorderobserver.Inthispaper,weproposetodecouplethecurrentobserverfromthefluxobserversoastorealizeindependentconvergencerates.Then,theresistanceestimationalgorithmisappliedtobothDVCandIdVC.Inparticular,intheapplicationtoIdVCthefluxobserverneedsnotbeused,whichleadstoasimplerstructure.Meanwhile,independentconvergenceratesofcurrentobserverandfluxobserveryieldanimprovedperformance.Asuperiorperformanceinthetorqueandfluxresponsesinbothcasesisverifiedbynumeroussimulations.