[en] The fine structure of the vacuum UV photoabsorption spectrum of CH₃Br and CD₃Br has been analyzed in the 6.9-10.2 eV photon energy range. A large number of lines have been observed, classified and assigned to the vibrational excitation accompanying a series of Rydberg transitions. The effects of the Jahn-Teller distortion and of the spin-orbit splitting of the ground electronic state of the ion have been considered. The former effect has been evaluated by ab initio calculations, showing that the ²E state (in the C_3v symmetry group) splits into ²A' and ²A'' states in the C_S symmetry group. Even though the energy difference of about 1 meV is extremely small, the ²A' state is energetically the lowest component whereas the ²A'' is found to be a transition state. The Jahn-Teller stabilization energy and the wavenumbers associated with all vibrational modes have been calculated. Experimentally, the entire fine structure could be described in terms of three vibrational modes, i.e., hcω₄=146+/-6 meV (1178+/-48 cm^-1), hcω₅=107+/-6 meV (863+/-48 cm^-1) and hcω₆=71+/-4 meV (572+/-32 cm^-1), respectively, as resulting from an average over all analyzed Rydberg states. In CD₃Br the corresponding energies are hcω₄=104+/-3 meV (839+/-24 cm^-1), hcω₅=82+/-4 meV (661+/-32 cm^-1) and hcω₆=62+/-4 meV (500+/-32 cm^-1). These values are in fairly good agreement with those predicted by the present ab initio calculations for the ionic ground state. The experimental isotopic ratio ρ_i=[ω/ω_isot]_i is 1.15+/-0.14, 1.31+/-0.14 and 1.39+/-1.0 and is predicted to be 1.04, 1.34 and 1.36, respectively, for ω₆, ω₅ and ω₄. On the basis of the present study an alternative assignment of the CH₃Br⁺(X-bar ²E) photoelectron band structure is proposed