The problem of constructing multi-cast trees to meet the quality of service requirementsof real-time interactive applications operating in high-speed packet-switched environments is presented.Inparticular,the new concept of the delay is redefined,that is,the concepts of delay of the link (or the path)and delay of destination are distinguished.Routineend-to-end delay is defined as "deadline delay" or"bounded delay" and the delay of number of tardymember in this paper is defined as "slack delay".Theslack delay of the destination refers to the feature thatthe accumulated delay from the source to any destina-tion along the tree may exceed the value of slack delay.The problem of determining such a constrained tree isNP-complete.A heuristic presented demonstrates agood average case behavior in terms of the two objec-tives.We also show that it is possible to dynamicallyreorganize the initial tree in response to changes in thedestination set,in a way that is minimally disruptiveto the multicast session.