The study of Superstring Theories on AdS backgrounds is important in the context of Gauge/Gravity correspondence. These theories can be reduced, under certain assumptions, to Sigma Models on semi-symmetric super-cosets. For a peculiar class of these cosets one can also introduce a WZW term. This correspond to study a Superstring Theory on a background supported by a mixture of RR and NSNS fluxes, as can happen for theories on $AdS_3\times S^3 \times M_4$. I will show the effect of this term on Integrability, Kappa symmetry and conformality of the theory, computing also the BMN spectrum in some relevant case for $AdS_3/CFT_2$ correspondence.