Purpose: Physical education has been described as an essential material to contribute to sustainable development. Therefore, it is necessary to examine the proficiency of higher education students in the three dimensions of sustainable development. This paper aims to analyse both the competences associated with the sustainability of preservice physical education teachers and the curriculum's influence on them. Design/methodology/approach: In total, 341 students (112 women) completed the validated Physical Education for Sustainable Development--Future Teacher PESD-FT questionnaire. This instrument assesses sustainable competences in its three dimensions (social, economic and environmental). In order to determine the influence of the curriculum on sustainability competences, the academic year studied was used as a variable. Variables such as gender, age and competitive experience in institutionalised sport were also considered in the statistical analysis. Findings: The results showed that the total set of students scored above average in their self-perception of competences associated with sustainable development in all three dimensions. The Mann-Whitney U test and Kruskal-Wallis statistics showed no differences attributed to gender and grade, respectively. Originality/value: This could help to rule out the influence of the curriculum as the main factor in the acquisition of these sustainable competences. However, greater competitive experience in institutionalised sports was associated with greater proficiency in social competence within sustainable development.