Nanoindentation tests have been conducted on five different polyolefins, comprising a high density polyethylene, a low density polyethylene, a linear low density polyethylene, a polypropylene homopolymer and a polypropylene copolymer. The nanoindenter was fitted with a "Dynamic Stiffness Measurement" (DSM) facility that permits measurement of storage modulus and loss modulus at frequent intervals during an indentation test. The results were quite scattered, especially those for the loss modulus, and methods of processing the data to derive meaningful results were examined and are discussed. The storage modulus measurements were found to give the same stiffness ranking as the monotonic load-displacement data when comparing indentations on the same material. Some correlation was found between the storage modulus and fractional crystallinity. An averaging procedure was developed for the loss modulus values that appeared to give a consistent assessment of the dissipation properties of the different materials. Analysis of the monotonic component of the load-displacement data indicated that the nature of the deformation changed from mainly elastic/viscoelastic to mainly viscoelastic/plastic during the course of the indentation tests. POLYM. ENG. SCI., 46: 1160 -1172, 2006.