The collective excitations in doped short-period GaAs/AlAs superlattices were studied. An extremely small broadening of the plasmon-LO phonon collective modes caused by the coherent collective response of the electron plasma was detected in an unexpectedly high range of doping levels. The observed spectral narrowing accompanied by a pronounced red-shift of the relevant Raman lines was found, in good qualitative agreement with the theoretical prediction that the cooperative behaviour of the interacting localized electrons is responsible for the established effects. The behaviour of the parameters associated with the collective excitations indicates the formation of coherent dynamic clusters similar to those known to exist in ferroelectrics. The coherent clusters were found to disappear both with the increase of doping (abruptly) and the increase of temperature (gradually).