This paper examines the problem of quality-of-service group communications in a heterogeneous network, which consists of multiple mobile ad hoc networks attached to the backbone Internet. A heuristic multicast algorithm named delay and delay variation multicast algorithm (DDVMA) is proposed. DDVMA is designed for solving the delay- and delay-variation-bounded multicast tree problem, which has been proved to be NP-complete. It can find a multicast tree satisfying the multicast end-to-end delay constraint and minimizing the multicast delay variation. Two concepts, which can help the DDVMA achieve better performance in terms of multicast delay variation than the delay and delay variation constraint algorithm that is known to be the most efficient so far, are proposed, namely, 1) the proprietary second shortest path and 2) the partially proprietary second shortest path. An analysis is given to show the correctness of DDVMA, and simulations are conducted to demonstrate the performance improvement of DDVMA in terms of multicast delay variation. It is also shown that the strategy employed by DDVMA is also applicable to handling the mobility of mobile hosts in a heterogeneous network