A model based on the van der Pol equation has been developed to predict the pattern of adaptation of aircrew and other travellers to rapid time-zone transitions, when the exposure to light cannot be quantified. The parameters of the model include the stiffness (mu) and the intrinsic period (T0), which together define the free-running period, and the external force (F). The parameter values were estimated by using a simplex minimization technique to fit the output from the model to body temperature data from 12 individuals before, and over a 12-day period immediately after, a 10-h eastward transition between London and Sydney. Data were collected at three equally spaced points during each sleep period and at the end of four 45-min rest periods during the day. The fitting procedure enabled the parameters of the temperature rhythm to be estimated after correcting for the masking effect of sleep. The average estimates of mu (0.38 h) and T0 (24.24 h) were close to earlier estimates based on forced desynchronization experiments, and the mean free-running period, calculated from these, was 24.50 h. The mean value of the external force F (0.54) was surprisingly high, and this may reflect the strong outdoor light levels during the days in Sydney. Estimates of phase, based on the model solutions, suggested that 11 subjects adapted by a phase delay and 1 by a phase advance. However, the amplitude of the rhythms was much reduced at times when the phase was changing rapidly. Simulations using the range of the model parameters for the 12 individuals predicted that adaptation to within 1 h after a 10-h eastward transition would be achieved within between 3 and 11 days. However, since these predictions are dependent on the choice of external force, estimates may need to be more conservative in real-life situations when light exposure cannot be measured.