On the basis of self-determination theory, we aimed to identify students' perceptions of interpersonal teaching style profiles (i.e. within-teacher combinations of six dimensions of need-supportive and need-thwarting behaviours of autonomy, competence and relatedness) and to examine, through a cross-sectional design, the possible associations between these teaching profiles and students' behavioural and emotional engagement. Participants were 2065 students (n[subscript teachers] = 38) of Physical Education (PE) (M[subscript age] = 11.96 ± 1.95; range = 10-16 years; 1042 girls) nested in 98 classrooms from elementary (n = 915) and secondary (n = 1150) Spanish schools. Students filled out questionnaires in a paper and pencil format during the last semester of the school year. A four-cluster solution was found to be the most suitable: (a) a high-low group (i.e. high in perceived need-support and low in need-thwarting), (b) a low-high group (i.e. low in perceived need-support and relatively high in need-thwarting), (c) a low-low group (i.e. low in both need-support and need-thwarting) and (d) a mixed group (i.e. low in autonomy support, high in autonomy-thwarting and relatively modest-to-high in competence and relatedness support and thwarting). A multivariate analysis of variance (MANOVA) indicated significant differences in students' behavioural and emotional engagement as a function of cluster membership. Post hoc comparisons showed that the high-low group reported the highest levels of engagement and the low-high group the lowest ones. Furthermore, the mixed group scored the second highest level of engagement -- higher than the low-low and the low-high group. These results suggest that teachers who fail to support students' needs for autonomy, competence and relatedness -- either by using or not using need-thwarting instructional practices -- might undermine students' engagement.