The nature of the next pandemic influenza virus, and particularly its reproduction number, is uncertain. If its reproduction number is low (R,2.0), our results indicate that at-risk countries receiving a reasonably small number of travelers (say 400 per day) from the infected source region can expect a natural delay until importing an epidemic of the order of 2 months. This is quite variable and under favourable conditions it could be 4 months. However, the natural delay decreases rapidly as R increases.