Prediction-error-methods tailored for state space model based predictive control are presented. The prediction-error methods studied are based on predictions using the Kalman filter and predictors for a linear discrete-time stochastic state space model obtained from a continuous-discrete-time stochastic transfer function representation. Both single-step and multi-step prediction-error methods based on least squares, maximum likelihood and maximum a posteriori criteria are derived and presented. It is argued that the prediction-error criterion should be selected such that it is compatible with the objective function of the predictive controller in which the model is to be applied. Realization of the discrete-time stochastic state space model from a continuous-discrete-time linear stochastic system specified using transfer functions with time-delays is outlined. The proposed prediction error-methods are demonstrated for a SISO system parameterized by the transfer functions with time delays of a continuous-discrete-time linear stochastic system. The simulations for this case suggest to use the one-step-ahead prediction-errormaximum-likelihood (or maximum a posteriori) estimator. It gives consistent estimates of all parameters and the parameter estimates are almost identical to the estimates obtained for long prediction horizons but with consumption of significantly less computational resources. The suitability of the proposed method for predictive control is demonstrated for dual composition control of a simulated binary distillation column.