Real-time services, including constant bit rate (CBR) and real-time variable bit rate traffic (rt-VBR), have become increasingly important owing to the rapid proliferation of multimedia applications. A cell multiplexing method capable of handling real-time traffic should satisfy related quality of service (QoS) requirements, including cell transfer delay (CTD), cell delay variation (CDV) and cell loss ratio (CLR). In this paper, we present an efficient cell multiplexing method, called longest delay beyond expectation (LDBE), to schedule real-time and non-real-time traffic in ATM networks. For the real-time traffic, LDBE scheme can minimize the CDV, and reduce the CLR and CTD, particularly when different CDV tolerance (CDVT) values are applied at each node along the path of a connection. Simulation results demonstrate that the proposed LDBE performs better than other multiplexing methods regarding these CLR, CDV and CTD criteria for real-time traffic. Furthermore, the proposed LDBE is also suitable for scheduling non-real-time traffic by providing a low CLR for non-real-time variable bit rate (nrt-VBR) and minimizing the CTD for unspecified bit rate (UBR) traffic.