The equilibrium structures of FNO, ClNO, HONO, and FNO2 have been determined using three different, somewhat complementary methods: a completely experimental, a semi-experimental (where the equilibrium rotational constants are derived from the experimental effective ground-state rotational constants and an ab initio cubic force field), and an ab initio, where geometry optimizations are usually performed at the coupled cluster level of nonrelativistic electronic structure theory using small to very large Gaussian basis sets. For the sake of comparison, the equilibrium structures of HNO and N2O have also been redetermined, confirming and extending earlier results. The semi-experimental method gives structural parameters in good agreement with the reliable experimental results for each compound investigated. Because of inadequate treatment of electron correlation, the single-reference CCSD(T) method gives N-X (X[double bond]F, Cl, OH) bonds that are too strong and associate bond lengths that are significantly too short. The discrepancy increases with increase in the size of the basis set. A much more elaborate treatment of electron correlation at the CCSDTQ level solves this problem and results in increased bond lengths, correctly representing the weakness of the N-X bond in these XNO and XNO2 species. The equilibrium structures determined are accurate to better than 0.001 A and 0.1 degrees .