Bouc-Wen　hysteretic　model　is　widely　used　to　describe　the　nonlinear　characteristics　for　structural　systems.　However,　the　restoring　force　is　expressed　by　differential　form　of　the　displacement,　which　makes　it　difficult　to　analyze　dynamic　responses　by　substituting　the　hysteresis　model　into　the　governing　equation　of　motion.　Assuming　that　the　restoring　force　is　the　exponential　function　of　the　displacement　and　that　the　non-linearity　is　weak,　a　direct　expression　is　adopted　instead　of　Bouc-Wen　differential　model.　Furthermore,　a　power　series　expression　by　the　polynomial　of　the　displacement　is　educed　using　Thaler＇s　expandedness.　Taking　several　representative　examples,　trajectories　of　hysteretic　loops　and　dynamic　response　curves　of　single-degree-of-freedom　systems　are　obtained　and　compared　well　with　the　results　of　the　Bouc-Wen　differential　model　in　order　to　examine　the　validity　of　the　present　polynomial　expression.　The　results　draw　quite　a　lot　agreement,　especially　for　the　second-order　approximations　and　the　systems　with　softening　behavior.