This paper studies the dynamic behaviour of a railway wheelset in different operating conditions, and investigates the effect of traction sub-system on the stability and performance of the wheelset. The system studied combines the conventional wheelset with a traction subsystem and a wheelset stabilisation control subsystem. The mathematical model of the wheelset including the two control sub-systems is presented. The issues of stabilising the wheelset passively or actively are discussed and the detail of the traction control is given. A comprehensive analysis is made to study characteristics of the wheelset and more importantly interactions between the wheelset control and the traction subsystem. One of the key conclusions from the study is that the conventional passive solutions for the wheelset instability is reasonably robust in the presence of tractive effort and traction dynamics, whereas some of the newly proposed active control approaches require more careful considerations.