This study identified and discussed principals' perceptions of acceleration and enrichment for gifted students. These areas have proven significant for the teaching of the gifted. The research questions included questions about perceptions of giftedness and how principals organize to allow gifted students to develop and learn based on their conditions and needs. The empirical material consisted of open questions where the informants freely could describe their knowledge and perceptions about gifted students and their education. The principals' mission statement formed the theoretical basis for analysis. The method used was content analysis. Previous research has shown that acceleration and enrichment are significant for teaching and learning for gifted students. It is therefore of importance that principals, responsible for the activities of the schools they are responsible for, are aware of these and enable the teachers to work with acceleration and enrichment based on the different needs of the gifted students. The results showed that the principals in the study believed that (a) acceleration should primarily take place in the gifted students' age-appropriate class, (b) second by studying subjects or courses with higher classes, (c) third, that the teachers enable enrichment for gifted students in their age-appropriate class, (d) fourth, grade skipping is complicated and should be avoided.