The exponential growth in tourist numbers motivates serious analysis of this phenomenon. The econometric methods commonly used do not take this central feature of demand seriously in the form and estimating of tourism demand models. Cointegration analysis has been used in recognition of the problem as a technical estimation issue. But this is unsatisfactory, due to both technical methodological concerns with the use of cointegration analysis and because it overcomes the growth issue rather than incorporating it into the model. A model form which does incorporate growth is proposed. Other, newer methods – neural networks and structural equations modelling – are sometimes applied, but these too are not unproblematic.