Summary: A prediction method is given for a first- and second-order nonstationary spatio-temporal process. The predictor uses local data only and consists of a two-stage generalized regression estimate of the local drift at the prediction location added to a kriging prediction of the residual process at that location. This predictor is applied to observations on seasonal, rainfall-deposited sulfate over the conterminous United States between summer 1986 and summer 1992. Analyses suggest that predictions and estimated prediction standard errors have negligible to small biases, there is spatially heterogeneous temporal drift, and temporal covariance is negligible.