Collective communications play an important role in parallel computing. Many features of an ATM(asynchronous transfer mode) switch environment can be exploited in the design of collective operations. In this paper, the authors present a collective communications framework based on ATM——hybrid-tree, which fully takes advantage of the features supporting multicast of ATM and is suitable to implement collective communications in dynamic groups. The problems of the maintance of the hybrid-tree are completely solved by the group management protocol and methods to maintain the hybrid-tree presented in this paper.