This paper has analysed the import demand for virgin olive oil in the EU and more precisely in the Italian market, as it concentrates more than 80% of EU imports, aiming to determine the relative position of Mediterranean EU and non-EU countries exports and their degree of substitutability or complementarity. The methodology used is based on the specification of a Threshold Almost Ideal Demand System in which special attention has been paid to the stochastic properties of the series involved. In an empirical context, the paper has aimed to provide a set of import demand elasticities that can be useful in trade models. Results point to Spain as the leader in the Italian virgin olive oil market. It is expected that this position will be maintained in the future. Greece has improved its relative position after its accession into the EU. However, imports coming from Greece are highly dependent on the situation in Spain. Tunisia has good potential for future exports development as a consequence of new perspectives of trade liberalisation taking into account its relative position in the Italian market, in spite that its exports are currently constrained due to existing quotas.