In　this　paper,　an　efficient　method　using　the　linear　moments　(L-moments)　is　proposed　for　dynamic　reliability　assessment　of　nonlinear　structures　subjected　to　non-stationary　ground　motions.　The　proposed　method　comprises　three　main　steps.　First,　the　extrema　of　structural　responses　are　obtained　from　the　random　function-spectral　representation　model　(RFSRM)　and　nonlinear　time　history　analysis,　in　which　the　principal　points　are　first　combined　with　the　RFSRM　and　a　sampling　strategy　is　suggested　to　determine　the　final　samples　of　extrema　by　deleting　close　values.　Second,　after　the　samples　of　extrema　are　obtained,　the　first　four　L　moments　can　be　estimated　from　their　definitions.　Finally,　using　the　first　four　L-moments　of　extrema　of　structural　responses,　the　probability　distribution　of　extrema　is　approximated　by　a　cubic　normal　distribution　based　on　the　L-moments　and　the　corresponding　failure　probability　of　a　nonlinear　structure　is　calculated.　Three　numerical　examples　are　presented　to　demonstrate　the　efficiency,　accuracy,　and　usefulness　of　the　proposed　method　for　the　dynamic　reliability　assessment　of　nonlinear　structures,　and　the　conventional　spectrum　representation　method　and　subset　simulation　method　are　used　for　comparison.　?　2021　Elsevier　Ltd.　All　rights　reserved.