Supermembrane compactified on a M9×T2 target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in SL(2,Z) when they correspond to the nontrivial central charge sector and they are trivial otherwise. The first ones contain eight inequivalent classes of M2-brane bundles which at low energies are in correspondence with the eight type II gauged supergravities in 9D. The relation among them is completely determined by the global action of T-duality which interchanges topological invariants of the two tori. The M2-brane torus bundles are invariant under SL(2,Z)×SL(2,Z)×Z2 . From the effective point of view, there is another dual invariant theory calaled Double Field Theory which describe invariant actions under O(D,D). Globally it is formulated in terms of doubled 2D torus fibrations over the spacetime with a monodromy given by O(D,D,Z). In this seminar we discuss T-duality global aspects considered in both theories and we emphasize certain similarities between both approaches which could give some hints towards a deeper relationship between them.