This paper describes the research conducted in the Republic of Croatia during the 2012/13 academic year. We have gathered opinions from experts, i.e. teaching methods teachers from seven faculties of teacher education, regarding the music teaching competencies necessary for primary education teachers teaching music in the first several grades of elementary school. We used the "Delphi method" in our research, i.e. in our sample survey among teaching methods teachers. The teachers also evaluated the competencies of their students and some elements of teacher education studies course syllabi and programmes. The sample survey among the teachers was implemented via email. The goal of the research was to determine if the programmes of the music courses at the teacher education studies are appropriate for the development of the competencies necessary for students of music education. Teaching methods teachers emphasized the need for more practical training, primarily regarding playing instruments and singing, and they pointed out that the course Teaching Methods in Music is the most important course for the training of future music teachers. Aside from that, they believe that more classes should be devoted to music courses, i.e. they propose to reorganise the contents of the courses by increasing the amount of practical classes and reducing the amount of theory classes. They also believe that it is necessary to introduce testing of musical ability at entrance exams for admission into the teacher education studies.