Favorable, nonequivalent canonical structures for a given free radical may correspond to local minima on the ab initio potential surface of the ground electronic state, The isomerization path between two such structures involves the relocation of an unpaired electron and coincident transformation of the donor and acceptor molecular orbital hybridizations. In ab initio calculations, this may cause convergence to a local minimum. In experiments, the relatively flat bending potential will complicate the vibrational energy level structure. Self-consistent field (SCF) and configuration interaction (CISD) calculations were employed in a search for multiple minima on the potential energy surfaces of seven X(2)A’ free radicals : NC2O, FC3O, ClC3O, HC3NH, HC4H2, HC2N2, and FC4H2. Minima were assumed to lie near the acetylenic, cumulenic, or allylic canonical forms. All of the three- and four-carbon compounds in this set exhibit at least two minima on the SCF potential surface. At the CISD level, two stable structures were identified for ClC3O and HC4H2, and three were found for FC4H2 In all cases, bending amplitudes of more than 40 degrees are classically allowed at energies less than 3000 cm(-1) above the global minimum potential energy. Ramifications of these potential surfaces are discussed, and a crude energy additivity comparison is presented. Predicted stationary point geometries, permanent dipole moments (mu), Fermi contact terms (alpha), and isomerization barriers are given.