Advanced nuclear magnetic resonance (NMR) techniques were applied to study the local environments of hydrogen in NaAlH(4). Through a combined application of the magic echo (ME) and the magic Hahn echo (MHE) sequences the hetero- and homonuclear contributions to the dipolar second moment (M(2)) were determined separately. The obtained values are compared with the second moments calculated by the van Vleck formulae, using structural data determined by neutron scattering on NaAlD(4). This comparison indicates structural differences between NaAlH(4) and NaAlD(4). A model is suggested for the orientation of the [AlH(4)](-) tetrahedra in NaAlH(4), for which the calculated second moments are in good agreement with the experimentally observed values.