This paper describes new approaches to generalized predictive control formulated in the delta (delta) domain. A new delta-domain version of the continuous-time emulator-based predictor is presented. It is shown to contain the optimal discrete-time predictor based on incomplete information as a special case. Usually, a good estimate is obtained in a much longer range of samples than obtained by the optimal predictor of the same complexity. This is particularly advantageous at fast sampling rates where a ’conventional’ predictor is bound to become very computationally demanding. Two controllers are considered : one having a well-defined limit as the sampling period tends to zero, the other being a close approximation to the conventional discrete-time GPC. Both algorithms are discrete in nature and well-suited for adaptive control. The fact that S-domain models are used does not introduce an approximation since such models can be obtained by exact sampling of continuous-time models.