The electronic structure of γ phase in the system Mg(17)Al(12) containing 58 atoms per unit cell with space group I43m has been calculated by using the WIEN2k-FLAPW program package. A pseudogap is found across the Fermi level. The FLAPW-Fourier spectra at the symmetry points N and Γ of the bcc Brillouin zone revealed that electronic states across the Fermi level at these symmetry points are dominated by |G|(2) = 26 and 24 states corresponding to centers of {510} + {431} and {422} zone planes, respectively. The 1253-wave nearly-free-electron (NFE) band calculations identified that a combination of the two Fermi surface-Brillouin-zone (FsBz) interactions associated with |G|(2) = 26 and 24 account well for the observed DOS pseudogap in γ-Mg(17)Al(12), most likely leading to the stabilization of this complex metallic compound. The β-Al(3)Mg(2) containing 1178 atoms per cubic unit cell is suggested to be stabilized by satisfying the Hume-Rothery matching condition expressed in terms of e/uc, the number of electrons per unit cell, versus critical |G|(2). A critical |G|(2) is predicted to be 200 in β-Al(3)Mg(2), which results in 84 Brillouin zone planes interacting almost simultaneously with a more or less spherical Fermi surface.