Nonparametric regression is developed for data with both a temporal and a cross-sectional dimension. The model includes additive, unknown, individual-specific components and allows also for cross-sectional and temporal dependence and conditional heteroscedasticity. A simple nonparametric estimate is shown to be dominated by a GLS-type one. Asymptotically optimal bandwidth choices are justified for both estimates. Feasible optimal bandwidths, and feasible optimal regression estimates, are also asymptotically justified. Finite sample performance is examined in a Monte Carlo study.