Rapid economic growth in South-East and East Asia has seen a surge in tourist arrivals from this region to Australia in the 1990s, prior to the currency crisis in late 1997. The purpose of the paper is to use Autoregressive Integrated Moving Average (ARIMA) models to explain the nonstationary seasonally unadjusted quarterly tourist arrivals from Hong Kong and Singapore to Australia from 1975(1) to 1996(4). As the tourist arrivals series display strong seasonal patterns, deterministic and stochastic seasonality are examined as possible explanations for variations in the international tourist arrivals series. The Hylleberg et al. (Journal of Econometrics, 99, pp. 215-38, 1990) test for seasonal unit roots is used to examine stochastic seasonality in the various series.