Since 1980, the cruise industry has recorded an impressive average passenger growth rate of approximately 7% per annum. From a methodological point of view, the evolution of the cruise traffic in a port system has been investigated by the academia using basic statistics, classical concentration ratios or strategic positioning analysis. The application to these techniques at compositional data (i.e. traffic share) may lead to erroneous conclusions and spurious correlations. Exploratory techniques considering the compositional character of the data are used in other disciplines to investigate potential correlation trends and similarity of compositional data. This research investigates the traffic share evolution of the cruise passengers in the Mediterranean ports from 2005 to 2016 using Compositional Data techniques (CoDa). Three multi-port regions based on geographical criteria are defined (i.e. East, West and Adriatic). Centered log-ratio transformation is used to formulate the compositions in a suitable basis and treating the coordinates of the compositions with the standard tools, based on the Euclidean distance. The temporal periods obtained from the hierarchical clustering using clr-transformations for the multi-port regions show a clear differentiated pattern in function of the traffic share evolution. Also, the periods obtained in the clustering analysis suggest periods consistent with the traffic share fluctuations coherent with the deconcentration processes in the market. The analysis proves that the CoDa methodology is useful to investigate the complexity of the dynamics of the traffic evolution in the port cruise system being the methodology applicable elsewhere in the context of port system analysis.