Type-I or type-II behaviour of the F_A centres in alkali halides has always been thought of as a feature dependent on the crystal lattice parameter and on the impurity size. We have found experimental evidence suggesting for the first time that both behaviours are present in RbCl:Li⁺, where the F_A centre at low temperature (T < 15 K) exhibits a luminescence of type-I switching to type-II at higher temperature. This effect is probably related to the possibility for the Li⁺ ion of being, at high temperature, a mobile and off-centre ion. Both these conditions seem to be necessary for having a type-II behaviour.