The geometries, the harmonic vibrational frequencies, and the Renner-Teller parameter have been reported for the NCO+((X) over tilde (3)Sigma(-)), NCO((X) over tilde (2)Pi,($) over tilde(A) over tilde (2)Sigma(+),(B) over tilde (2)Pi,2 (2)Sigma(+)), NCO-((X) over tilde (1)Sigma(+)), CNO+((X) over tilde), CNO((X) over tilde (2)Pi,(A) over tilde (2)Sigma(+),(B) over tilde (2)Pi,2 (2)Sigma(+)), and CNO-((X) over tilde (1)Sigma(+)) systems at the full valence-complete active space self-consistent-field (fv-CASSCF) level of theory. The (2)Pi electronic states of the NCO and CNO radicals have two distinct real vibrational frequencies for the bending modes and these states are subject to the type A Renner-Teller effect. The total energy of CNO+ without zero point energy correction of the linear geometry is similar to31 cm(-1) higher than the bent geometry at the fv-CASSCF level and the inversion barrier vanishes after the zero point energy correction; therefore, the ground state of the CNO+ may possess a quasilinear geometry. The spin-orbit coupling constants estimated using atomic mean field Hamiltonian at the fv-CASSCF level of theory are in better agreement with the experimental values. The excitation energies, the electron affinity, and the ionization potential have been computed at the complete active space second order perturbation theory (CASPT2) and the multireference singles and doubles configuration (MRSD-CI) levels of theory. The computed values of the electric hyperfine coupling constants for the N-14 atom in the ground state of the NCO radical agree well with the experimental data. The magnetic hyperfine coupling constants (HFCC's) have been estimated employing the configuration selected MRSD-CI and the multireference singles configuration interaction (MRS-CI) methods using iterative natural orbitals (ino) as one particle basis. Sufficiently accurate value of the isotropic contribution to the HFCC's can be obtained using an MRS-CI-ino procedure. (C) 2004 American Institute of Physics.