The paper studies the dynamics of economic growth caused by an increase in the growth rate of tourism demand. We develop a simple dynamic model of a small open economy, which is completely specialized in the production of tourism services (island economy model), populated by a large number of intertemporally optimizing agents, deriving utility from consuming an imported good. Tourism services are produced by means of a simple AK technology by using imported capital, its accumulation associated with adjustment costs. Moreover, the economy can lend or borrow at the international financial markets at the given world interest rate. Adjustments in the relative price of tourism services ensure market clearance for tourism services. The long-run growth rate of the economy is tied to the growth rate in tourism demand. An increase in the latter increases thus the economy’s long-run balanced growth rate. In contrast to the standard one-good small open economy endogenous growth model, where the economy is always on its balanced growth path, we show that there are transitional dynamics after an increase in the growth rate of tourism demand. In particular, the short-run growth rate of output rises gradually towards its higher long-run level, and the market price of tourism increases during transition. Thus, an increase in the growth of tourism demand, say, caused by higher economic growth abroad, leads to a boom in the small open economy and increasing terms of trade. Adjustments of the relative price of tourism services (i. e. the real exchange rate) can therefore not protect the economy from demand disturbances.