Bullying in State Greek Cypriot Primary Schools has been receiving a subsequent media attention in recent years. However, there is still not adequate research evidence on this issue. This study is an attempt to examine whether bullying could be considered as a form of aggressive behaviour, to investigate the situation in State Greek Primary Schools in Cyprus and to examine the developmental history, the psychological and social characteristics of nine 11- year-old bullies in State Greek Cypriot Primary Schools. These investigations were undertaken on the basis of four models: the Proposed Model of Aggression, the Model of the Empirical Work, the Model of Parents’ Perceptions about the bullies or bullying and the Model of the Teachers’ Perceptions about bullies or bullying. The study employed both qualitative and quantitative methods and comprised two stages. In Stage 1 a survey was undertaken of the teachers’ perceptions about bullying in 29 state primary schools in Nicosia. Pupil perceptions were surveyed in three schools where the levels of bullying seemed to be higher than in the rest of the schools. In Stage 2 a sample of 9 boys were identified as bullies from these 3 schools with high levels of bullying and these formed the case studies. An investigation of the nine boys’ developmental history, psychological and social characteristics was undertaken through interviewing their parents, teachers and peers and by the use of standardised tests and role play. This investigation of the nine case studies provided support for the view that bullying is a form of aggressive behaviour as all the factors that are reported in the relevant literature about aggression seem to play a role in its development, albeit to a different extent and in different combinations in the nine bullies. Moreover, bullying was found to occur in all State Greek Cypriot Primary Schools regardless of the social background of the school. Many factors related to the bullies’ psychological and social characteristics are involved in an act of bullying and consequently each has to be seriously taken into consideration, both individually and in combination, in any effort aiming at the prevention or inhibition of the problem in schools.