A　new　multiobjective　topology　optimization　method　for　compliant　mechanisms　with　geometrical　nonlinearity　is　presented.　Geometrically　nonlinear　structural　response　is　calculated　using　a　Total-Lagrange　finite　element　formulation　and　the　equilibrium　is　found　using　an　incremental　scheme　combined　with　Newton-Raphson　iterations.　The　multiobjective　topology　optimization　problem　is　established　by　the　minimum　compliance　and　maximum　geometric　advantage　to　design　a　mechanism　which　meets　both　stiffness　and　flexibility　requirements,　respectively.　The　weighted　sum　of　conflicting　objectives　resulting　from　the　norm　method　is　used　to　generate　the　optimal　compromise　solutions,　and　the　decision　function　is　set　to　select　the　preferred　solution.　The　solid　isotropic　material　with　penalization　approach　is　used　in　design　of　compliant　mechanisms.　The　sensitivities　of　the　objective　functions　are　found　with　the　adjoint　method　and　the　optimization　problem　is　solved　using　the　method　of　moving　asymptotes.　These　methods　are　further　investigated　and　realized　with　the　numerical　examples,　which　are　simulated　to　show　the　availability　of　this　approach.