A systematic ab initio MO study employing effective core potentials on the central atoms has been carried out to predict C-2v, C-4v, D-4h, and T-d structures and the corresponding energies and stabilities as well as periodic trends in these molecular properties for the series of hypervalent (hypercoordinated) XH(4)(-) and XF(4)(-) anions, where X = P, As, Sb, and Bi. The comparative all-electron calculations for the C-2v and C-4v, structures of these species with X = P, As, and Sb were also done. The lowest energy forms for both XH(4)(-) and XF(4)(-) were those of C-2v symmetry. All XF(4)(-)(C-2v) were found to be minima on the SCF potential energy surfaces, whereas the inclusion of electron correlation (MP2) changed the nature of PH4-(C-2v) and AsH4-(C-2v) from unstable transition states (TS) to stable minima. D-4h forms of XH(4)(-) and PF4- appeared to be TS’s for inversion of the C-4v forms; on the other hand, XH(4)(-)(C-4V) and XF(4)(-)(C-4v) were found themselves to be TS’s connecting C-2v minima. The energy decomposition analysis was used to clarify the periodic trends in both the E(C-4v) - E(C-2v) energies for XH(4)(-) and XF(4)(-) and in the thermodynamic stabilities of these species relative to loss of H- or F-.