Circular covariance patterns arise naturally from many important biological and physical processes. Modelling these patterns can be immensely important for proper analyses. In this article, we propose a circular linear exponent autoregressive (LEAR) correlation structure for cyclical longitudinal data. Special cases of this parsimonious correlation model include the equal correlation and first-order moving average (MA(1)) correlation structures and a circular analogue of the continuous-time AR(1) model. We discuss properties and estimation of the circular LEAR model in the context of cyclical longitudinal data concerning diet and hypertension (the DASH study). Analysis of these data exemplifies the benefits of the circular LEAR correlation structure. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.