The　subharmonic　resonance　response　of　the　strongly　nonlinear　delay　differential　equation　is　solved　using　the　incremental　harmonic　balance　method.　The　value　of　the　exciting　frequency　when　the　subharmonic　resonance　occurs　is　discussed.　The　influences　of　the　time　delay　and　the　feedback　gain　on　the　system　subharmonic　resonance　response　are　studied.　The　variation　of　the　subharmonic　resonance　response　with　the　system　parameters　is　obtained.　The　results　show　that　the　value　of　the　exciting　frequency　when　the　subharmonic　resonance　occurs　is　affected　by　the　system　parameters.　The　proportion　of　the　one　third　harmonic　in　the　amplitude　increases　rapidly　with　the　increase　of　the　exciting　frequency.　The　variation　of　the　amplitude　ratio　of　the　one　third　harmonic　and　the　first　harmonic　is　wavy　type.　The　proportion　of　the　one　third　harmonic　in　the　amplitude　decreases　with　increasing　the　displacement　feedback　gain　and　increases　with　increasing　the　velocity　feedback　gain.　The　proportion　of　the　one　third　harmonic　in　the　amplitude　occupies　a　dominant　position　in　the　subharmonic　resonance　response.