A sophisticated spin-vibronic model was developed to study electronic and nuclear dynamics in twofold degenerate electron systems. Eigenenergies and eigenfunctions of a model Hamiltonian are calculated in a basis set of products of electronic, electron spin, and vibrational functions. The X 2 E ground electronic state of the CH 3 O pyramidal (C 3v ) system has been studied with the simultaneous treatment of spin-orbit coupling, all linear and quadratic Jahn-Teller interactions including multimode couplings, and anharmonic effects up to the sixth order for the CH-stretching. The group-theoretical analysis of the spin-vibronic Hamiltonian and its eigenfunctions was performed in terms of irreducible representations (E 3/2 and E 1/2 ) of the double C 3v symmetry group. Vibronic and anharmonic model parameters of X 2 E CH 3 O were calculated with numerical differentiation using ab initio energies of the CH 3 O geometries distorted on normal coordinates. The equation-of-motion coupled cluster method with augmented core-valence basis sets of triple-quality was applied in these calculations. The value of the spin-orbit splitting in X 2 E CH 3 O was calculated using multiconfiguration quasidegenerate second-order perturbation theory with a complete active space reference wave function followed by a perturbative calculation of eigenvalues of the full Breit-Pauli spin-orbit operator.