Computer simulations have been made of large extensive air showers initiated by nuclei heavier than protons. The work forms part of a study of future experiments designed to identify the nature of the energetic primary particles. A model based upon data from nuclear emulsion experiments has been used to represent the break-up of the primary nuclei in collision with air nuclei. Differences in shower characteristics are predicted which are dependent upon the choice of model for the fragmentation of the primary nucleus and its energy. The major cause of fluctuations in the longitudinal development of showers produced by heavy particles is shown to be the pattern of the fragmentation of the incident nucleus. In the absence of a precise knowledge of the high-energy interaction, we have not identified any parameter in large showers which, if measurable and averaged over many showers, will reflect strongly the nature of the primary particle.