Magneto-Electro-Elastic　(MEE)　Composites,　as　an　innovative　functional　material　blend,　are　composed　of　multiple　materials,　boasting　exceptional　strength,　rigidity,　and　an　extraordinary　magneto-electric　interaction　effect.　This　paper　establishes　a　nonlocal　modified　couple　stress　(NL-MCS)　magneto-electro-elastic　nanobeam　dynamic　model.　To　accurately　capture　the　intricate　influences　of　scale　effects　on　nanostructures,　This　model　meticulously　examines　scale　effects　from　two　distinct　perspectives:　leveraging　nonlocal　elasticity　theory　to　elucidate　the　softening　phenomena　in　nanostructures　stemming　from　long-range　particle　interactions,　and　employing　modified　couple　stress　theory　to　reveal　the　hardening　effects　attributed　to　the　rotational　behavior　of　particles　within　the　structure.　By　incorporating　Von　Karman　geometric　nonlinearity,　Reddy＇s　third-order　shear　deformation　theory　and　Maxwell＇s　equations,　the　governing　equations　for　the　nonlinear　free　vibration　of　MEE　nanobeams　are　derived　using　Hamilton＇s　principle.　Finally,　a　two-step　perturbation　method　is　employed　to　solve　these　equations.　Two-step　perturbation　method　disintegrates　the　solution　process　into　two　stages,　iteratively　approximating　and　refining　the　solution,　thereby　progressively　unraveling　the　intricate　details　and　enhancing　the　precision　of　the　solution　in　a　systematic　manner.　Finally,　the　nonlinear　free　vibration　behavior　of　MEE　nanobeams　is　explored　under　the　coupled　magnetic-electric-elastic　fields,　with　a　focus　on　the　effects　of　various　factors　that　including　length　scale　parameters,　nonlocal　parameters,　Winkler-Pasternak　coefficients,　span-to-thickness　ratios,　applied　voltages　and　magnetic　potentials.