Misbehaviour detection is critical to the implementation of a secure and reliable V2X communications system. Vehicle or roadside unit misbehaviour is a potential threat to every vehicle and pedestrian using V2X communications, as misbehaviour could induce dangerous actions by other components within the V2X network. The Misbehaviour Authority has been identified as a necessary component in the Security Credential Management System (SCMS), the backend security infrastructure for V2X applications, but there is no defined standard at this time. This paper will define characteristics and core features that should be found in the Misbehaviour Authority, vehicle onboard units, and roadside infrastructure. This paper will also analyze several use cases for misbehaviour, and analyze the time for the SCMS to recognize misbehaviour and disseminate the information to other vehicles in the network. The analysis will provide an estimate for how long a misbehaving device will remain a threat to others before becoming blacklisted to all V2X devices. The goal of this paper is to create awareness and spark a discussion for this important part of the SCMS and security in V2X applications.