Respiratory syncytial virus (RSV) is the most common cause of acute lower respiratory tract infection in children. In this paper we use models of RSV transmission to interpret the pattern of seasonal epidemics of RSV disease observed in different countries, and to estimate epidemic and eradication thresholds for RSV infection. We compare the standard SIRS model with a more realistic model of RSV transmission in which individuals acquire immunity gradually after repeated exposure to infection. The models are fitted to series of monthly hospital case reports of RSV disease from developed and developing countries. The models can explain many of the observed patterns: regular yearly outbreaks in some countries, and in other countries cycles of alternating larger and smaller annual epidemics, with shifted maxima in alternate years. Previously these patterns have been attributed to the transmission of different strains of RSV. In some countries the timing of epidemics is not consistent with increased social contact among school children during term time being the major driving mechanism. Climatic factors appear to be more important. Qualitatively different models gave equally good fits to the data series, but estimates of the transmission parameter were different by a factor of 4. Estimates of the basic reproduction number (R(0)) ranged from 1.2 to 2.1 with the SIRS model, and from 5.4 to 7.1 with the model with gradual acquisition of partial immunity.