Nonlinear　dynamic　response　of　magneto-electro-elastic　(MEE)　laminated　nanoplates,　considering　both　the　flexomagnetoelectric　(FME)　effect　and　the　hygrothermal　effect,　are　investigated.　The　nonlinear　dynamic　model　for　MEE　laminated　nanoplates　has　been　formulated,　leveraging　the　high-order　shear　deformation　theory　(HSDT)　and　the　Hamiltonian　principle.　The　von　Karman　equation　is　employed　to　accurately　account　for　the　geometric　nonlinearities　inherent　in　the　system.　The　incorporation　of　the　nonlocal　strain　gradient　theory　(NSGT)　facilitates　the　precise　capturing　of　size-dependent　behaviors　pertinent　to　nanoplates.　The　Airy　stress　function　is　utilized　to　effectively　manage　and　simplify　these　intricate　nonlocal　nonlinear　terms　within　the　governing　equations.　The　nonlinear　time　history　response　(NTHR)　curves　of　the　MEE　laminated　nanoplates　are　acquired　by　utilizing　the　Galerkin　method,　iterative　method,　and　Newmark　method.　Based　on　this,　the　nonlinear　dynamic　response　of　the　MEE　laminated　nanoplate　is　analyzed　in　detail,　including　the　FME　effect,　size　parameters,　various　physical　field　parameters,　external　load,　and　elastic　foundation　coefficient.　The　results　of　this　study　provide　valuable　insights　into　the　precise　design　of　smart　nanostructures　incorporating　MEE　laminated　nanoplates.