The stability of the pumping discharge for XeCl (Ne/Xe/HCl) lasers is investigated by using different one-dimensional models, considering both bulk discharge instabilities and filamentary ones. It is found that the bulk stability in a XeCl laser discharge can be improved, under certain conditions, due to the vibrational excitation of HCl molecules : this effect is studied by using different models for the HCl vibrational kinetics. It is established that the very short instability time found in experiments cannot be explained as a result of bulk instability of the discharge. On the other hand a satisfactory comparison with experiments can be obtained by adding to the model a simplified microinstability which develops in the discharge.