Group key exchange protocols are basic protocols to provide privacy and integrity in secure group communication. This paper discusses the security of one type of group key exchange protocols and defines the kind of protocols as broadcaster group protocols. It points out two attacks on this kind of protocols. The first attack can be avoided by using fresh values in each action during one session of the group protocol. The second attack should be related with concrete application. It also proposes a dynamic key agreement protocol as an example of solutions at the last part of the paper. Group paper exchange the protocols are basic protocols to provide privacy and integrity in secure group communication. This paper discusses the security of one type of group key exchange protocols and defines the kind of protocols as broadcaster group protocols. It points out two attacks on this kind of of protocols. The first attack can be avoided by using fresh values ​​in each action during one session of the group protocol. The second attack should be related with concrete application. It also proposes a dynamic key agreement protocol as an example of solutions at the last part of the paper.