The structures, energetics, spectra, and bonding of the isomers BeNH and HBeN are described theoretically at the ab initio Hartree-Fock and configuration interaction levels. The species HBeN is still unknown experimentally, and the results reported in this paper represent the first theoretical prediction of its existence. For the molecule BeNH, vibrational frequencies with an unequivocal assignment of the NH stretching are the only experimental data found in the literature. In contrast with the scarceness of experimental information, and complementing previous studies on BeB, BeC, BeN, and BeF, this paper reports detailed results on geometries, vibrational frequencies, relative stabilities, excited electronic states, and electronic rearrangements leading to the bonding in the molecules BeNH and HBeN. The molecule BeNH is 10.5 kcal/mol more stable than HBeN, and the favorite route for dissociation involves breaking the Be-N bond in both BeNH and HBeN. The three lowest electronic states in BeNH are very closely spaced with the first excited singlet state (1PI) only about 1500 cm-1 higher than the ground state (1SIGMA+); in contrast, for HBeN the first 3PI is about 8000 cm-1 higher than the 3SIGMA- ground state. Their vibrational frequencies are quite distinct, and the predicted values for HBeN will certainly allow an unequivocal identification of this species. As to the bonding in the molecule BeNH, an unexpected 2s2 --> 2p(x)1 2p(y)1 electronic promotion leads to a pi-type bond between the beryllium and nitrogen atoms which is not found in the isomer HBeN. In both molecules a significant ionic character also contributes to the bonding between these two atoms.