It　is　often　unable　to　distinguish　between　transient　and　steady-state　responses　for　those　of　aseismic　structures.　Here,　the　empirical　mode　decomposition　(EMD)　method　was　used　to　decompose　a　structural　response　into　several　intrinsic　mode　functions　(IMFs),　and　based　on　the　half-wave　simple　harmonic　feature　of　IMF　and　the　harmonic　wave　theory,　a　half-wave　quasi-simple　harmonic　analysis　method　was　proposed　to　realize　separation　of　seismic　transient　and　steady-state　responses.　Transient　responses,　steady-state　ones　and　response　spectra　of　long-period　and　short-one　structures　under　different　types　of　earthquakes　were　studied.　Results　showed　that　the　characteristics　of　their　transient　and　steady-state　responses　under　action　of　broadband　seismic　signals　are　different　from　those　under　action　of　single-component　seismic　signal;　transient　responses　and　steady-state　ones　of　structures　with　different　periods　under　different　types　of　earthquakes　play　an　important　role　in　the　total　displacement　response,　and　both　of　them　are　mutually　restricted;　if　one　of　the　two　responses　is　ignored,　the　total　response　can　be　over-estimated　to　make　structural　design　be　conservative　and　uneconomic.　©　2020,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.