This paper presents an investigation into the non-steady rolling contact mechanics within the context of railway wheel-rail contact. The focus is on the relationship between the creep force and non-steady parameters, and the purpose is to examine whether a linear system exists for these non-steady cases. The non-steady contact parameters under investigation are contact geometry, normal force, and creepage. Both the normal and tangential contact problems were solved using previously developed time-domain models based on Kalker's [Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990] numerical theory for half-space contact with prescribed, mainly sinusoidal, load histories. The resultant creep forces were then analysed with a system identification method in order to find a possible transfer function to provide linear representations of the non-steady contact behaviour. It was found that although linear models can be identified in some cases, a general, simple linear model cannot be realised in practice and the non-steady rolling contact mechanics is generally non-linear.