This article investigates the degree of persistence in the international monthly tourist time series in Spain using long memory (fractional integration) techniques. Our findings can be summarized as follows. The two standard hypotheses of integer degrees of differentiation, i.e., the I(0) and the I(1) behaviour, are clearly rejected. The series is found to be I(d) with a value of d in the interval (0.421, 0.780) thus implying long memory behaviour and mean reverting behaviour. However, if a structural break is considered, it takes place at May 2007, and then, the two subsamples present orders of integration which are above 1 and thus rejecting the mean reverting hypothesis.