Magnetoelectroelastic　(MEE)　materials,　as　smart　composites　consisting　of　piezoelectric　and　piezomagnetic　phases,　exhibit　distinct　phenomena:　the　piezoelectric　phase　generates　a　flexoelectric　effect,　and　the　piezomagnetic　phase　induces　a　flexomagnetic　effect.　Hence,　understanding　the　influence　of　the　flexomagnetoelectric　(FME)　effect　on　the　mechanical　characteristics　of　these　materials　during　their　application　is　crucial.　This　article　investigates　the　nonlinear　free　oscillation　response　of　MEE　laminated　nanoplates,　considering　the　FME　effect　and　elastic　foundation,　in　hygrothermal　environments.　The　derivation　of　the　nonlinear　dominant　equations　for　the　MEE　laminated　nanoplate　with　hydrothermal　environments　has　been　accomplished,　grounded　in　the　principles　of　Hamilton’s　principle,　nonlocal　strain　gradient　theory　(NSGT),　and　the　higher-order　shear　deformation　theory　(HSDT).　Employing　the　Airy　stress　function　serves　as　a　means　to　handle　the　complexities　arising　from　the　nonlinear　nonlocal　terms.　Moreover,　the　control　equations　are　tackled　by　a　combined　approach　that　incorporates　both　the　two-step　perturbation　method　(TPM)　and　the　Lindstedt-Poincare　perturbation　method　for　their　solution.　The　TPM　can　obviate　the　necessity　for　making　hypotheses　or　conjectures　concerning　the　configuration　function.　Specifically,　the　effects　of　FME　effects,　NSGT　parameters,　elastic　foundation　parameters,　dimensional　parameters　of　the　nanoplate,　and　various　physical　field　parameters　on　the　nonlinear　free　oscillation　properties　of　the　MEE　nanoplate　are　meticulously　examined.　The　findings　of　this　study　demonstrate　significant　application　potential　in　the　fields　of　nanosensors,　actuators,　and　energy　harvesters.　©　2024　IOP　Publishing　Ltd.　All　rights,　including　for　text　and　data　mining,　AI　training,　and　similar　technologies,　are　reserved.