Abstract: In IP ATM internetworking, edge devices are used to connect IP and ATM subnets physically. To support IIS services, edge devices, functioning as a proxy, setup VC connections inside the ATM subnet to support the IIS services QoS requirements including services mapping between the IIS service model and the ATM QoS model. A service mapping solution is given in the paper. And based on the ideal stream model, formulas are deduced which use the buffer of edge devices to influence the stream description parameters mapping.