International and domestic tourism are leading economic activities in today's world. Tourism has been known to generate goods and services directly and indirectly, attract foreign currency, stimulate employment and provide opportunities for investment. It has also been recognized as an important means of achieving economic development. Substantial research has been conducted to evaluate the role of international tourism, and its associated volatility, within and across various economies. This paper applies several recently developed models of multivariate conditional volatility to investigate the interdependence of international tourism demand, as measured by international tourist arrivals, and its associated volatility in the four leading destinations in ASEAN, namely Indonesia, Malaysia, Singapore and Thailand. Each of these countries has attractive tourism characteristics, such as significant cultural and natural resources. Shocks to international tourism demand volatility could affect, positively or negatively, the volatility in the tourism demand of neighbouring countries. The empirical results should encourage regional cooperation in tourism development among ASEAN member countries and also mobilize international and regional organizations to provide appropriate policy actions.