The standard damping model is the viscous dashpot for which the damping force is proportional to velocity. However, this simple model seems not to reflect real conditions where there may be viscoelastic effects, friction or air resistance. No general models for damping are available that can be developed from first principles and used in computer simulations. To help with this difficulty the fundamental theory that should underpin any general damping model is assembled here. The only available formulation for damping in mechanics is the Rayleigh dissipation model that can be used with Lagrange’s equation. This model is strictly viscous and linear. The possibility of using this model for all damping circumstances is examined. A starting point for the development of a theory is the need for causality. This need is used to formulate the concept of a pure dashpot (i.e. not mixed with other dynamic components) which is shown to be viscous. Furthermore in order to represent damping in general it is necessary to embed the viscous dashpot with other mechanical components which are not dissipative and are either linear or nonlinear. It appears that even for non-linear systems the only form of damper that is possible is the linear viscous dashpot.