This article shows how multilevel modelling can be used to study institutional variations in the gender differences in achievement. The results presented are from analyses of the degree classifications of 22,433 individuals who graduated in mathematical sciences, from universities in the UK, between 1994/95 and 1999/2000. The analyses were designed to measure gender differences in the achievement of first class honours in mathematical science degrees as a whole and within individual institutions. After allowing for students' entry qualifications, age, type of course and institution attended, no systematic gender difference was detected in the achievement of first class honours in mathematical sciences at any level of entry qualifications. However, there were statistically significant variations between universities in "gender difference added". This variation between institutions in gender difference added was explained by the significant gender differences in the first class degree awards made by Oxford and Cambridge universities, with no significant evidence of gender differences in the first class degree awards made by other institutions.