We consider nonparametric estimation of an additive time series decomposition into a long-term trend 𝜇 and a smoothly changing seasonal component S under general assumptions on the dependence structure of the residual process. The rate of convergence of local trigonometric regression estimators of S turns out to be unaffected by the dependence, even though the spectral density of the residual process has a pole at the origin. In contrast, the rate of convergence of nonparametric estimators of 𝜇 depends on the long-memory parameter d. Therefore, in the presence of long-range dependence, different bandwidths for estimating 𝜇 and S should be used. A data adaptive algorithm for optimal bandwidth choice is proposed. Simulations and data examples illustrate the results.