Nonparametric estimation of a mean trend function for replicated time series is considered. The ith series is defined by Y_i(j) = g(t_j)+g_i(t_j)+X_i(j) (J=1,2,3,...) with ∑g_i=0. The error processes X_i(i=1,…,k) for the individual series are assumed to be stationary with fractional differencing parameters _∈(-12,12 ) , corresponding to anti-persistence (δ_i < 0), short-range dependence (δ_i = 0) or long-range dependence (δ_i > 0). A non-parametric estimate of g is defined. The optimal bandwidth and optimal integrated mean squared error are derived under the assumption of fixed and randomly generated δ_i’s, respectively. Simulations illustrate the results.