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Spanish Mediterranean coasts are a consolidated tourist destination and enjoy growing demand. These coasts receive the highest number of international arrivals in Spain. This paper has been developed to gain a better knowledge of the determinants of this international tourism demand. A nonlinear dynamic model that analyses how previous tourists can affect tourism demand decisions is proposed. This nonlinear dynamic specifi cation extends the standard dynamic equation for tourism demand to include interaction effects between previous tourists and two destination characteristics: the quality of the tourism services and tourist congestion. Both characteristics are important to defi ne the reputation or attractiveness of the destination. We test the model using panel data from the 11 provinces which make up the Spanish Mediterranean coasts, and the 7 European countries which are the main origin markets for the period 2005-2015. The system GMM procedure is applied to estimate the econometric model. The econometric results show evidence of strong persistence in international tourism demand. Previous tourists have an important positive and non-constant effect, and this effect is positively infl uenced by the quality of the tourism services, and negatively by tourist congestion. Therefore, the effect of previous tourists is not constant but varies across provinces and over time. This effect is stronger in provinces with high quality tourism services and lower congestion. Additionally, the impact of previous tourists has not remained constant over time, but has increased in the Mediterranean provinces since 2005. The investments realized in quality and quantity of hotel services during this period have enhanced their reputation.