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Group key agreement is a fundamental building block for the increasing number of collaborative applications. The protocol is more complicated than peer-to-peer communication owing to its dynamic characteristics, but the research to date on group key agreement protocols (GKAP) mainly focuses on static security, the most distinctively dynamic characteristic of GKAP being difficult to analyse by existing methods. The paper attempts to extend the strand space theory to analyse the dynamic security of GKAP. With the aid of the theory, the AT-GDH protocol is taken as an example to discuss the general conditions of security retention in dynamic cases. A new scheme is proposed of updating the session key when some member leaves the group; it is based on SA-GDH.2 protocol to avoid the single-point weakness.