New species with molecular formula Si2N2, not yet observed experimentally, are described theoretically for the first time. Nine different stationary points have been examined and the effects of electronic correlation on the structural parameters, harmonic frequencies, and relative energies are described at increasingly higher levels of correlation treatment (MP2, MP4, CCSD(T)). The global minimum corresponds to a linear singlet state ((1) Sigma(g)(+)) SiNNSi. At the CCSD(T) level, the next most stable species (at 15.08 kcal/mol) has a nonclassical tetrahedral-like structure similar to the global minimum of Si2H2. This is followed by another local minimum with a linear structure SiNSiN (at 20.25 kcal/mol) and by a rhomboidal-type structure (at 21.33 kcal/mol), which is in fact a transition state connecting two equivalent tetrahedral-like structures. Another nonclassical structure similar to the monobridged one in the case of Si2H2 was also found to be a local minimum (at 28.18 kcal/mol). An interconversion path from this latter structure to the linear SiNNSi one is likely to occur via another transition state located at about 38 kcal/mol. With the exception of the linear isomer SiNNSi, the triplet states were found to lie very high energetically and to correspond to unstable structures. None of these species exhibits any appreciable amount of silicon-silicon bonding, and the analogue of cyanogen (NCCN) NSiSiN is unstable. The nature of the bonding in the most relevant species is also discussed, as well the energetics of dissociation. An analysis of the energetics and structural similarities and differences between Si2N2, C2N2, Si2H2, and Si2C2 is also carried out. Caution must be exercized in generalizing results at a low level of theory since they have not been confirmed by the CCSD(T) calculations.