By　the　nonlocal　theory,　the　nonlinear　equations　for　double-layered　nanoplates　(DLNP)　with　different　boundary　conditions　are　established.　The　relation　between　aspect　ratio　and　nonlinear　frequencies　with　fixed　mode　amplitude　is　discussed.　This　relation　for　two　vibration　modes　presents　completely　distinct　trends.　The　novel　fact　is　observed　that　there　exists　a　point　P　where　nonlinearity　is　weakest　for　the　fundamental　mode.　Furthermore,　we　notice　that　P　only　appears　for　clamped　movable　edge　when　neglecting　the　nonlocal　effect,　which　is　substantially　different　from　the　other　boundary　conditions.　It　should　distinguish　whether　the　edge　is　movable　or　immovable　for　studying　nonlinear　dynamics　of　DLNP.　(C)　2015　Elsevier　B.V.　All　rights　reserved.