Structures　under　parametric　load　can　be　induced　to　the　parametric　instability　in　which　the　excitation　frequency　is　located　the　instability　region.　In　the　present　work,　the　parametric　instability　of　double　walled　carbon　nanotubes　is　studied.　The　axial　harmonic　excitation　is　considered　and　the　nonlocal　continuum　theory　is　applied.　The　critical　equation　is　derived　as　the　Mathieu　form　by　the　Galerldn＇s　theory　and　the　instability　condition　is　presented　with　the　Bolotin＇s　method.　Numerical　calculations　are　performed　and　it　can　be　seen　that　the　van　der　Waals　interaction　can　enhance　the　stability　of　double-walled　nanotubes　under　the　parametric　excitation.　The　parametric　instability　becomes　more　obvious　with　the　matrix　stiffness　decreasing　and　small　scale　coefficient　increasing.　The　parametric　instability　is　going　to　be　more　significant　for　higher　mode　numbers.　For　the　nanosystem　with　the　soft　matrix　and　higher　mode　number,　the　small　scale　coefficient　and　the　ratio　of　the　length　to　the　diameter　have　obvious　influences　on　the　starting　point　of　the　instability　region.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.