PurposeIn　the　context　of　rapid　nanotechnology　advancements,　size　effects　have　become　key　in　determining　material　performance.　In　order　to　better　investigate　the　impact　of　size　effects　on　nanostructures,　a　new　nonlocal　modified　couple　stress　(NL-MCS)　model　developed　for　magneto-electro-elastic　(MEE)　nanobeams　is　introduced　in　this　research.　This　model　comprehensively　incorporates　size-dependent　effects,　prominently　reflecting　the　softening　characteristics　introduced　by　the　nonlocal　elasticity　theory　(NL),　while　also　accounting　for　the　influence　of　modified　couple　stress　(MCS)　on　hardening.　The　model　incorporates　von　Karman＇s　geometric　nonlinearity　theory,　Reddy＇s　third-order　shear　deformation　theory　and　Maxwell＇s　equations.　The　objective　of　this　paper　is　to　analyze　the　dynamic　response　behavior　of　MEE　nanostructures,　providing　a　theoretical　foundation　for　the　design　and　mechanical　response　of　MEE　nanostructures.MethodsThe　Galerkin　method　is　employed　to　process　the　dynamic　model　of　MEE　nanobeams,　followed　by　iterative　solution　of　the　processed　model　using　the　Newmark　method.　Additionally,　quadratic　extrapolation　is　utilized　to　enhance　the　convergence　rate　of　the　iterative　process.Results　and　ConclusionA　comprehensive　analysis　of　the　influences　of　material　length　scale　parameter,　nonlocal　parameters,　Winkler-Pasternak　coefficients,　aspect　ratio,　volume　fraction　of　materials,　applied　magnetic　potential　and　applied　voltage　on　the　nonlinear　dynamic　response　of　MEE　nanobeams　are　conducted.