The Spanish autonomous city of Melilla, located in northwest Africa, has one of the highest academic failure and abandonment rates in Europe. An effective way to improve this situation would be to improve students' digital competence. In order to do so, teachers must have competent digital skills themselves and also be able to teach them. To determine teachers' level of digital competence, the Spanish adaptation of the European Framework for Digital Competence of Educators was used to analyse the self-assessment responses of teachers in training at the Faculty of Education and Sport Sciences in Melilla, Spain. Several quantitative techniques were used to analyse data collected from a questionnaire based on the items in the framework. Indicators were given to each competence using a factor analysis to contrast differences between undergraduate and postgraduate students. Correlations between some of the students' characteristics and the competences were estimated using OLS. The results show students' self-assessment level of digital competence in different areas and differences between the bachelor's and master's programmes. Digital competence gaps were also detected in teacher training, especially in security. The conclusions highlight the need to improve digital security and facilitate a higher level of digital skills in line with the framework. Indeed, more hours of training in digital competence are required while taking into account the educational context and the technological, pedagogical and content knowledge needed to teach. Equally, the same skills must be developed by educators in order for them to transmit digital competence to their students and support them in educational centres.