In application layer multicast (ALM) tree, when a parent node quits or fails, all its descendent nodes must adjust their positions, which causes the interruptions of multicast connections. This problem is called stability problem of ALM trees, and it may affect the continuity of multicast data transmission and then degrade user experience seriously. This paper first analyzes the stability problem of ALM trees and proposes the instantaneous stability degree model (ISDM). An approach which takes advantage of the statistical properties of members’ join-leave behaviors is proposed to estimate the relative leave probability of member nodes in ISDM. Then, real-time transmission is one of the important aspects of ALM and one major objective of the ALM-based real-time transmissions is to determine multicast tree so as to guarantee the lower delay. This paper proposes the DDSD (the degree-and delay-bounded maximum instantaneous stability degree ALM tree) problem based on the ISDM. The DDSD problem is proved to be NP-Hard and an approximation algorithm (i.e. DDSD-H) is proposed to solve it. In addition, three heuristic policies are presented for the algorithm. Finally, the simulation results demonstrate the validity of the proposed algorithms and the comparison in the performance of the three heuristic policies is made.