The existence of a series of triatomic molecules with the general formula MNM', where M is an alkaline metal (K, Rb, Cs), and M' is an alkaline earth metal (Ca, Sr, Ba), has been predicted by quantum chemical methods. Among these, the CsNBa molecule shows a feature not found before, the presence of a multiple bond between barium and nitrogen. As a consequence of this novel bonding situation, the molecule is linear. The same holds for all Ba triatomics, MNBa, independent of the nature of the alkali M atom, and for all Sr compounds, MNSr. The presence of a multiple bond makes CsNBa, and other related Ba and Sr molecules, particularly stable and appealing experimentally. The systems with the alkaline earth metal M' = Ca, on the other hand, turned out to be bent. Calculations have also been performed on the negative ions BaN- and CaN-, which form a well-defined entity in the MNM' systems (M' = Ba, Ca). The results show that the two ions have a different electronic structure in the ground state, which is one reason for the different properties of the MNM' systems and explains why the molecules containing the BaN- moiety are linear, while those containing CaN- are bent.