This paper demonstrates the importance of adequately modelling the Underlying Energy Demand Trend (UEDT) and seasonality when estimating transportation oil demand for the UK and Japan. The structural time series model is therefore employed to allow for a stochastic underlying trend and stochastic seasonals using quarterly data from the early 1970s, for both UK and Japan. It is found that the stochastic seasonals are preferred to the conventional deterministic dummies and, more importantly, the UEDT is found to be highly non-linear for both countries, with periods where it is both upward and downward sloping.