In recent years, there have been increasing calls for greater support for high-achieving students in Germany, particularly in response to the results of international large scale assessments such as TIMSS and PISA. However, more knowledge about the characteristics of this group of students is required in order to develop suitable approaches to promote high achievement. This dissertation investigates exemplarily for science which characteristics of students, teaching and teachers contribute to the particular achievement at the end of primary school. The results show that the subject-related self-concept, cognitive abilities and teacher support are significant predictors. Measures to promote high achievement should therefore focus on these three aspects.