This paper addresses some advances in the theoretical description of molecular spectroscopy beyond the Born - Oppenheimer adiabatic approximation. A solution of the nuclear dynamics problem complicated by the E circle times E Jahn - Teller effect and spin - orbit coupling is considered for the case of the CF3O and CF3S radicals, all the model parameters being obtained solely from ab initio calculations without any adjustment to experimental numbers. Vibrational and vibronic model parameters were calculated at the equation-of-motion coupled cluster level of theory with basis sets of triple-zeta quality. The spin -orbit coupling in X E-2 CF3O and CF3S was parametrized by means of a perturbative solution of the full Breit - Pauli spin - orbit operator. Spin-vibronic eigenvalues and eigenfunctions were computed in a basis set of products of electronic, electron spin, and vibrational functions. Results demonstrate the importance of explicit inclusion of the spin - orbit coupling and at least cubic Jahn - Teller terms in the model Hamiltonian for the high precision evaluation of spin-vibronic energy levels of CF3O and CF3S. The theoretical results support and complement the spectroscopic data observed for these species.