A multistep adaptive predictive control strategy based on a state space model of the process has been developed. It can he compared with the Generalized Predictive Control algorithm. The emphasis in the development of the proposed control scheme is on modeling and elimination of disturbances. In the proposed scheme any prior information regarding the disturbances can be incorporated (by specifying certain polynomials and/or the noise covariances). If no prior information is available then the unknown unmodeled effects (such as noise, unmeasured load-disturbances and model process mismatch) can be represented by a residual model which can best be identified in a two-stage setting. This approach leads to satisfactory modeling of disturbances and good regulation via predictive control. Some important features of the proposed algorithm are: (i) it uses a state space model which allows separate modeling of u-to-y process dynamics, process and measurement noise; this is not possible in an ARMAX-type input/output model where process and measurement noise appear lumped in the noise polynomial; (ii) it uses a Kalman Filter (KF) to generate the predictions of the output; the KF can be easily tuned via noise covariances and is a simpler and better alternative to specifying or estimating a noise polynomial; (iii) there is no need to solve a Diophantine identity on-line; the result is reduced computation; and (iv) if residual modeling is used it leads to simpler and improved way of handling disturbances. The proposed control algorithm is presented for the single-input, single-output case. Applying the algorithm to multivariable processes is straightforward. Simulation examples are included to illustrate the advantages and performance of the proposed control scheme.