Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries such as S_4, A_4 and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyse the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E_8 symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S_4, A_4 and their transitive subgroups, including the dihedral group D_4 and Z_2 X Z_2. We discuss various issues that emerge in the implementation of S_4, A_4 neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z_2 X Z_2 model.
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