Abstract. We consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve. In a recent paper [3], Bj¨ork and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations.