The paper aims to quantify the influence of non-steady-state tyre behaviour and suspension damping on the instantaneous response of a vehicle to handling manoeuvres. The influence of such parameters cannot be determined using steady-state tests. In the present work, a recently developed methodology is employed, which has been applied in the past to simple transient handling studies. Here, the approach is applied to more demanding situations and the effects of tyre lags and suspension damping are directly related to the under-, over, or neutral-steer character of the vehicle under test. To distinguish the effect of tyre force lags, tyre non-linearities and combined tyre-vehicle non-linearities, an increasingly complex approach is adopted, which involves the implementation of a linear bicycle-model, a nonlinear bicycle-model and a 10-DOF non-linear vehicle model. In all cases tyre force lags are simulated using the relaxation length concept. The 10-DOF vehicle model is validated against experimental measurements and forms the basis for fully non-linear studies. It is shown that even inherently under-steering vehicles may initially over-steer as a result of the delayed response of tyres. Finally, it is demonstrated that the proposed approach captures the effect of suspension damping and some problems are discussed regarding its application.