Mobility management has become a core function in internet services and networks as mobile devices have been widely used and their capabilities have dramatically advanced. It is expected that proxy mobile IPv6 (PMIPv6), which is the most prominent solution, will play an important role in supporting these devices' mobility. To protect PMIPv6 networks, several authentication schemes have been presented. However, due to their static approach, the existing schemes failed to keep a good balance between security and efficiency. Motivated by this, the authors study an adaptive authentication scheme for mobile devices in PMIPv6 networks. In particular, the proposed scheme considers mobile nodes' context information to decide authentication strength, based on which adaptive authentication is performed. It is shown from the formal security verification and the example study that the proposed scheme is not only correct, but also achieves a good trade-off between security and efficiency