tudeoftheascendingnodeand?isthelongitudeofperihelion.subscriptspandndenoteplutoandneptune. meanmotionresonancebetweenneptuneandpluto(3:2).thecriticalargumentθ1=3λp?2λnplibratesaround180°withanamplitudeofabout80°andalibrationperiodofabout2x104yr. theargumentofperihelionofplutowp=θ2=?p?Ωplibratesaround90°withaperiodofabout3.8x106yr.thedominantperiodicvariationsoftheeccentricityandinclinationofplutoaresynchronizedwiththelibrationofitsargumentofperihelion.thisisanticipatedinthesecularperturbationtheoryconstructedbykozai(1962). thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofneptune，θ3=Ωp?Ωn，circulatesandtheperiodofthiscirculationisequaltotheperiodofθθ3becomeszero，i.e.thelongitudesofascendingnodesofneptuneandplutooverlap，theinclinationofplutobecomesmaximum，theeccentricitybecomesminimumandtheargumentofperihelionbecomes90°.whenθ3becomes180°，theinclinationofplutobecomesminimum，theeccentricitybecomesmaximumandtheargumentofperihelionbecomes90°again.williamsbenson(1971)anticipatedthistypeofresonance，laterconfirmedbymilani，nobilicarpino(1989). anargumentθ4=?pn+3(Ωp?Ωn)libratesaround180°withalongperiod，～5.7x108yr. inournumericalintegrations，theresonances(i)–(iii)arewellmaintained，andvariationofthecriticalargumentsθ1，θ2，θ3remainsimilarduringthewholeintegrationperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargumentθ4alternateslibrationandcirculationovera1010-yrtime-scale(fig.17).thisisaninterestingfactthatkinoshitanakai's(1995，1996)shorterintegrationswerenotabletodisclose. 6discussion whatkindofdynamicalmechanismmaintainsthislong-termstabilityoftheplanetarysystem?，thereseemtobenosignificantlower-orderresonances(meanmotionandsecular)betweenanypairamongthenineplanets.jupiterandsaturnareclosetoa5:2meanmotionresonance(thefamous‘greatinequality’)，-orderresonancesmaycausethechaoticnatureoftheplanetarydynamicalmotion，buttheyarenotsostrongastodestroythestableplanetarymotionwithinthelifetimeoftherealsolarsysM.XＩaＰE.cＯＭ