Thispaperdealswithanalyticandnumericaldissipativityandexponentialstabilityofsingularlyperturbeddelaydifferentialequationswithanyboundedstate-independentlag.Sufficientconditionswillbepresentedtoensurethatanysolutionofthesingularlyperturbeddelaydifferentialequations(DDEs)withaboundedlagisdissipativeandexponentiallystableuniformlyforsufficientlysmallε>0.Wewillstudythenumericalsolutiondefinedbythelinearθ-methodandone-legmethodandshowthattheyaredissipativeandexponentiallystableuniformlyforsufficientlysmallε>0ifandonlyifθ=1.