The article focuses on twice-exceptional students; that is, to those students who, on the one hand, face either obstacles or deficiencies or disorders and are mostly referred to as students with special needs, and on the other hand are musically gifted. In order to get a slightly clearer insight into the music education of twice-exceptional students, some foreign and domestic studies are presented, focusing on different groups of musically gifted students who are also special needs students. Furthermore are summarized the basic findings of case studies from Slovenian music schools, conducted as part of a doctoral research. These show how basic music education is experienced by teachers, parents and students who have successfully showed musical talent by passing the preliminary exam, and at the same time have a variety of special needs.