This paper proposes a procedure to make efficient predictions in a nearly non-stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non-stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit-root pretest predictor. In the case of a process that has a zero mean, only the non-differenced predictor is slightly better than the proposed combination method. In the general case of a non-zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 John Wiley & Sons, Ltd.