A study of the fluctuations in the densities of N-particles in extensive air showers has been carried out with a set-up consisting of five N-detectors located at the centre of an array of scintillators. Air showers were grouped according to their size and the distance of the core from the N-detectors. In each group of showers of given size and core distance the observed frequency distribution in the number of N-detectors activated, shows the existence of large fluctuations in the densities of N-particles.