This paper deals with the implications for translator training in Spanish universities for multi-language situations. In order to situate the reader, the authors first refer to the political circumstances of the European Union, its linguistic policy, the academic cooperation activities it has promoted, and to the situation of translator training in Spain. Comments are made based on the authors' practical teaching experience at the University of Granada in the School of Translating and Interpreting. Granada is the monolingual Castilian-speaking of Andalusia, and for this reason the authors' experience differs from that of those translator training departments situated in bilingual parts of Spain, such as Catalonia, Valencia, etc., where courses usually include the possibility of working with two "A" languages or mother tongues.