Based　on　HHT　and　harmonic　earthquake　response　theory,　the　dynamic　properties　of　skyscraper　structures　under　seismic　motion　are　studied.　Using　model　superposition　method,　computation　and　analyses　of　earthquake　transient　response　of　MDOF　systems　are　conducted.　Different　characteristics　of　displacements　of　long-period　structures　and　short-period　structures　are　obtained,　and　criteria　put　forward.　The　study　of　the　dynamic　properties　of　a　high　chimney　under　seismic　motion　reveals　that　when　a　120-meter-high　chimney　is　subjected　to　earthquake　wave,　the　displacement　of　the　structure　above　50m　is　controlled　by　transient　vibration,　which　reflects　the　long-period　characteristics　of　displacement　response,　while　the　displacement　of　the　structure　below　50m　is　controlled　by　steady　vibration,　which　reflects　the　short-period　characteristics　of　displacement　response.