A model for the integrated moving averages process of order one, IMA (1, 1), having a seasonal (cyclic) component is presented. The model incorporates a parameter for possible change in level of the process after intervention, following methods developed by Box and Tiao (1965), and Glass, Willson, and Gottmann (1972). Least-squares estimates and associated significance tests for the parameters of the model (in particular, the intervention parameter) are derived. The results of a computer study and an example from real data are given with analysis and interpretation of parameter estimates. Results of the theoretical derivation are extended to other models [IMA (1, 1) with deterministic drift, multi-component models], and limitations of the model are noted. (Author)