To study non-durable import demand, we extend previous work done by Clarida (1994) and Ceglowski (1991) by considering a two-good version of the lifecycle model in which we introduce time-non-separability in the households' preferences. The model is estimated using quarterly data for the USA and France. Using the information contained in the observed stochastic and deterministic trends, we derive a cointegration restriction used to estimate curvature parameters of the instantaneous utility function. The remaining parameters are estimated in a second step by GMM. The constancy of the different parameters is investigated, in both the long and the short run. Habit formation turns out to be an important factor of import demand.