This study compares the performance of different Artificial Neural Networks models for tourist demand forecasting in a multiple-output framework. We test the forecasting accuracy of three different types of architectures: a multi-layer perceptron network, a radial basis function network and an Elman neural network. We use official statistical data of inbound international tourism demand to Catalonia (Spain) from 2001 to 2012. By means of cointegration analysis we find that growth rates of tourist arrivals from all different countries share a common stochastic trend, which leads us to apply a multivariate out-of-sample forecasting comparison. When comparing the forecasting accuracy of the different techniques for each visitor market and for different forecasting horizons, we find that radial basis function models outperform multi-layer perceptron and Elman networks. We repeat the experiment assuming different topologies regarding the number of lags used for concatenation so as to evaluate the effect of the memory on the forecasting results, and we find no significant differences when additional lags are incorporated. These results reveal the suitability of hybrid models such as radial basis functions that combine supervised and unsupervised learning for economic forecasting with seasonal data.