Since the turn of the century, universities have to cope with demands of internationalization; and more recently to cope as well with demands to educate for global citizenship, especially after the United Nations Secretary-General's Global Education First Initiative (GEFI) launched in September 2012. This paper reports an experience of training teachers to promote these aspects in a Mexican university. More precisely, to explore how far a group of university teachers, that were trained to promote internationalization, were from the main principles of global citizenship education. Their answers to a questionnaire specially designed for this purpose, were compared with the answers of a group of teachers, from the same university, who have not been trained in the mentioned matter. A test "U" of Mann-Whitney showed a significant difference between the two sets of answers, from which some reflections are derived and related actions are suggested for training university teachers. [For the complete Volume 16 proceedings, see ED586117.]