Based　on　the　criterion　for　minimizing　the　mean　square　of　equation　difference,　the　applicability　of　the　equivalent　models　with　linear　or　cubic　restoring　force　for　the　steady-state　displacement　response　of　hardening　spring　Duffing　systems,　subjected　to　Gaussian　white　noise,　was　approached.　The　results　show　that　the　equivalent　error　rate　depends　on　the　relative　hardening　stiffness　coefficient　η;　the　prediction　precision　of　the　linear　equivalent　model　declines　but　that　of　the　cubic　restoring　force　equivalent　model　improves　with　η　increasing;　η　has　one　critical　value　η0;　the　cubic　restoring　force　equivalent　models　have　the　same　prediction　precision　as　the　linear　one　when　η　=　η0;　and　for　η　>　η0,　the　cubic　restoring　force　equivalent　model　is　better　than　the　linearization　model.