The paper deals with the estimation of a simultaneous equation system with time-varying parameters. The system is formulated in state space form and it is shown that the Kalman filter algorithm is applicable. The prior information required by this estimation method can be obtained by maximization of the likelihood function via Fisher-Scoring. Applying and extending an approach due to Engle, Watson (1981) leads to the recursive calculation of the score and the information matrix for the model under consideration. Three simulation experiments are run to show that the proposed algorithm performs well with respect to the identification of time-varying parameters in a simultaneous equation model.