The authors have studied the saturation behaviour of the electron paramagnetic resonance (EPR) spectrum of defects in crystals when they undergo a reorientational motion with particular reference to the H_i⁰(Li) defect in MgO:Li. The EPR spectra of this centre have been measured as a function of temperature and microwave power. Two features appear as a consequence of the simultaneous presence of saturation and motion. The saturation degree of a particular line depends on its allowed or forbidden character and also on the extent to which motion affects that line. Different lines of a given spectrum can show different dependencies on microwave power. In order to understand this behaviour, they have performed a lineshape simulation analysis. The stochastic Liouville formalism, which has been extensively used in the nonsaturated case, has been extended to include saturation phenomena. Several approximations have been made to reduce the dimension of the problem. The calculations reproduce the experimental facts qualitatively, although a quantitative fitting has not been attempted owing to the presence of unresolved interactions that deform the lineshape.