Cyclical components in economic time series are analysed in a Bayesian framework, thereby allowing prior notions about periodicity to be used. The method is based on a general class of unobserved component models that allow relatively smooth cycles to be extracted. Posterior densities of parameters and smoothed cycles are obtained using Markov chain Monte Carlo methods. An application to estimating business cycles in macroeconomic series illustrates the viability of the procedure for both univariate and bivariate models.