A more detailed analysis is given here of the singularities in the E.S.R. spectrum of the trifluoromethyl radical in a polycrystalline matrix. Some of the unexplained ‘extra’ lines are interpreted as resulting from orientations such that some of the resonance fields are stationary as a result of ‘non-crossing’ of the manifolds of resonance fields due to second-order splitting. A calculation of the polycrystalline spectrum for a planar axial model of·CF3is presented, and shows that the second-order effect is of the right order of magnitude.