Because of the high-speed and QOS guarantees, ATM networks are getting popular in multimedia applications. There are multimedia applications that require messages to be delivered in an order that preserves cause and effect relations in multicasts (called causal order multicast). Causal order multicast algorithms introduce an overhead because they append control information to messages to enforce the causal order. In this paper, we present a framework for evaluating causal multicast algorithms. We present a causal multicast algorithm called the partition method that supports multicasting and has a low overhead. We compare and analyze its cost with the cost of two existing algorithms on ATM networks, called the causal order multicast and delta causal order multicast methods. This analysis is carried out for four different sample network topologies to represent different configurations.