The rotational structure of the previously observed (B) over tilde (2)A' <- (X) over tilde (2)A" and (B) over tilde (2)A' <- (A) over tilde (2)A' laser-induced fluorescence spectra of jet-cooled cyclohexoxy radical (c-C6H11O) [Zu, L.; Liu, J.; Tarczay, G.; Dupre, P; Miller, T. A. Jet-cooled laser spectroscopy of the cyclohexoxy radical. J. Chem. Phys. 2004, 120, 10579] has been analyzed and simulated using a spectroscopic model that includes the coupling between the nearly degenerate (X) over tilde and (A) over tilde states separated by Delta E. The rotational and fine structure of these two states is reproduced by a 2-fold model using one set of molecular constants including rotational constants, spin-rotation constants (epsilon s), the Coriolis constant (A zeta(t)), the quenched spin-orbit constant (a zeta(e)d), and the vibronic energy separation between the two states (Delta E-0). The energy level structure of both states can also be reproduced using an isolated-state asymmetric top model with rotational constants and effective spin-rotation constants (epsilon s) and without involving Coriolis and spin-orbit constants. However, the spin-orbit interaction introduces transitions that have no intensity using the isolated-state model but appear in the observed spectra. The line intensities are well simulated using the 2-fold model with an out-of-plane (b-) transition dipole moment for the (B) over tilde <- (X) over tilde transitions and in-plane (a and c) transition dipole moment for the (B) over tilde <- (A) over tilde transitions, requiring the symmetry for the (X) over tilde ((A) over tilde) state to be A" (A'), which is consistent with a previous determination and opposite to that of isopropoxy, the smallest secondary alkoxy radical. The experimentally determined (A) over tilde-(X) over tilde separation and the energy level ordering of these two states with different (A' and A?) symmetries are consistent with quantum chemical calculations. The 2-fold model also enables the independent determination of the two contributions to the (A) over tildeX similar to separation: the relativistic spin-orbit interaction (magnetic effect) and the nonrelativistic vibronic separation between the lowest vibrational energy levels of these two states due to both electrostatic interaction (Coulombic effect) and difference in zero-point energies (kinetic effect).