Penguin Engineering Ltd has developed a compact, efficient, hysteretic damping device, the Penguin Vibration Damper (PVD). Experimental test results show that the PVD can provide a significant amount of damping at displacements as small as 50 micro-metres. The hysteresis behaviour of the PVD can be described well either by a model having a linear spring in parallel with a viscous dashpot, or by a bi-linear model, with the parameters of both models being displacement-amplitude dependent. For large displacements, the bi-linear model gives an accurate representation of the PVD's hysteresis loops, and the parameters for the bi-linear model can be taken as constants. Non-linear models, such as the hyperbolic, Ramberg-Osgood and multi-surface plasticity models, can also be used and have an advantage of displacement-amplitude-independent parameters. However, it can be shown that nonlinear models do not correctly predict the amount of damping that a PVD provides at large displacement even though the equivalent spring coefficient can be well approximated. When the PVDs are expected to undergo large displacements, it is possibly best to use a simple bi-linear model in dynamic nonlinear structural analyses, because the bi-linear model with suitably selected parameters can produce the correct amount of damping derived from the experimental data. The changes of the PVD's dynamic behaviour are small after a fatigue test of 144 000 cycles with a displacement amplitude of 2 mm. An analysis of a 6-storey reinforced concrete moment resisting frame is used to demonstrate the effect of the damper. Equivalent first modal damping ratios are estimated for various levels of earthquake excitations. The example shows that the dampers can provide a large amount of damping to the structure and enhance the structural capacity, for resisting earthquakes, by 50-100%.