Excited states in ~27,128Xe were populated in the reaction 9Be+ t22Sn at E~ah=38 MeV. The de-excitation of the isomeric states 7/2 + in 127Xe and 8 in 128Xe was studied using angular distribution and TDPAD methods on molten 1228n targets. The results are T~/2(7/2+)=37+ 1 ns, g(7/2+)= +0.241 _+0.009The experimental g-factors suggest the main configurations vg7/2 and vh 11/297,2 for the isomeric states. Detailed analysis of the combined information from g-factors and transition rates set stringent limits on the admixtures of the wave functions. The quasirotational bands built on the two-quasiparticle 6 and 10 + states are extended to higher spins, (14--) and (16+), respectively, and their structures are analyzed within the framework of the Interacting Boson Model.