Summary Two general models for a queue in which groups of entities arrive at a single service line and are serviced in groups are defined. Various equilibrium properties for both models are established in terms of the traffic intensity ρ. For the special case of Poisson arrivals the first model is analyzed with reference to the imbedded Markov chain, the waiting time, and the busy period. It is demonstrated that if the entities arrive in groups the stationary distribution of the imbedded Markov chain does not agree with the general equilibrium distribution obtained by letting time t → ∞. For the special case of exponential service the stationary distribution of the imbedded Markov chain for the second model is obtained and the waiting time problem is discussed briefly.