In this paper, we address issues related to providing guaranteed real-time communication in ATM local area networks. We concentrate on output link scheduling because it plays a critical role in meeting message deadlines. We are particularly interested in the weighted round robin scheduling policy because of its simple design and implementation. To use weighted round robin scheduling for hard real-time applications, the weights must be properly allocated to each of the connections. We propose and analyze two weight allocation schemes. The first scheme is heuristic, and is easy to understand and implement. The second scheme is optimal. That is, it can always guarantee a set of hard real-time connections whenever it is possible to do so. We evaluate and compare the system performance in terms of its admission probability-the probability that deadlines of all connections in a randomly chosen connection set can be met. We find that the optimal weight allocation scheme indeed performs the best. However, the heuristic scheme performs closely to the optimal scheme over a wide range of loading conditions.