The structures and energetics of the N2O2 isomers are predicted at several levels of theory. Both single reference and multireference based correlated methods were used to determine the structures and relative energies. Five high-energy minima were located above 2NO with QCISD(T)/6-311+G(2df)//MP2/6-311 +G(d) (PT2F/6-311+G(2df)//MCSCF/6-31G(d)) relative energies of ca. 38 (51), 46 (51), 61 (74), 69 (74), and 68 (80) kcaymol for 1,2-diaza-3,4-dioxacyclobutene (1), bond stretch 1,3-diaza-2,4-dioxa[1.1.0]bicyclobutane (2), a-N2O2 (3), 4, and 1,3-diaza-2,4-dioxa[1.1.0]bicyclobutane (5), respectively. The effect of basis sets on structures is small within a given level of theory. The MCSCF structures agree reasonably with those of MP2.