Once with accession to the European Union, new requirements related to education at university level must be respected and promoted. Emphasis should be put on values such as tolerance, mutual respect, acceptance of otherness, and so on. These things imply that university teachers should possess multiple skills enabling them to promote among undergraduate students cultural values and intercultural communication, which leads to performance and progress for everyone involved in the educational system. But it is extremely difficult to achieve these goals if the intercultural competency is not correct defined or described. In this article we will try to discover the structure of intercultural competency in order to promote it among university teachers, for undergraduate students to achieve it, and to apply it in an educational context. (Contains 2 figures.)