In the current context of globalisation it seems inevitable that the international openness of universities would also lead to efforts to attract foreign students. In the case of Spain, this is more necessary, insofar as the drop in population, the existence of other quality educational offerings, and the greater number of public and private universities have made students a target to compete for. Cutbacks in public funds have accentuated this trend. This article analyses the international demand at Spanish universities in order to determine whether there are significant differences because of the level of local competition faced by universities and public or private ownership. The Herfindhal index and analysis of variance are used to this end. Using data from the Statistics on University Students for the 2005-2006 and 2011-2012 academic years, we found that the creation of the European Higher Education Area partially affected international demand at Spanish universities. The overall international attractiveness of the Spanish university system improved considerably and universities have assumed an international view, regardless of the competition in their respective areas. Therefore, local competition is no longer a decisive factor to explain the international demand. In contrast, although public or private ownership does not determine the international attractiveness of universities, it does serve to explain their type of international demand.