Thin fullerene-like CNx coatings deposited on hard substrates (e.g. SiC) show very shallow residual impressions when investigated by nanoindentation at displacements less than the coating thickness. The low work of indentation (i.e. the small area enclosed by the loading and unloading curves) of these materials implies a large amount of recovery of indent depth which is often associated with materials of high hardness. However, analysis of the unloading curves by the Oliver-Pharr method generates hardness values which are usually less than that of silicon. Detailed analysis of the loading curve shows three distinct regimes of behaviour corresponding to behaviour controlled by surface roughness, elastic deformation and plasticity. Measurements of Young's modulus from the elastic part of the loading curve, from the Oliver-Pharr method and from elastic wave measurements are all consistently low. This implies that the material behaves like a very hard rubber which undergoes considerable elastic recovery on unloading but does not have a very high resistance to penetration on loading. The very high H/E values for fullerene-like CNx confirms this view.