Current　inelastic　seismic　spectra　suffer　from　a　conceptual　limitation:　they　are　significant　only　on　the　maximum　demand　of　ductility　and　they　do　not　include　any　influence　of　the　number　of　response　cycles,　yield　excursions,　stiffness　and　strength　degradation　and　damage　potential　to　structures.　This　paper　presents　a　stochastic　approach　for　obtaining　damage-based　inelastic　seismic　spectra.　In　order　to　consider　the　cumulative　damage　phenomenon　in　structural　systems　under　strong　ground　motions,　the　authors　adopt　the　Park　and　Ang　damage　model　that　includes　the　displacement　ductility　and　the　hysteretic　energy.　The　novelty　is　that　the　peak　theory　of　random　processes　is　adopted　to　achieve　damage-based　seismic　spectra.　This　approach　has　some　advantages　compared　with　the　standard　statistical　approaches　based　on　a　large　number　of　recorded　accelerograms.　First,　it　drastically　reduces　the　computational　effort,　while　allowing　us　to　typify　the　seismic　motion　by　some　parameters　such　as　the　frequency　content,　peak　acceleration,　energy　content　and　strong　motion　duration,　i.e.　all　the　parameters　that　affect　the　structural　response　under　seismic　actions.　Besides,　it　allows　to　obtain　the　following　stochastic　inelastic　seismic　response　spectra:　damage-based　(i)　displacement　and　acceleration　inelastic　spectra,　(ii)　response　modification　factor　spectra,　(iii)　yield　strength　demand　spectra,　and　(iv)　damage-based　inelastic　displacement　ratio　spectra.　©　2017　World　Scientific　Publishing　Company.