In this paper we propose a parametric and a non-parametric identification algorithm for dynamic errors-in-variables model. We show that the two-dimensional process composed of the input-output data admits a finite order ARMA representation. The non-parametric method uses the ARMA structure to compute a consistent estimate of the joint spectrum of the input and the output. A Frisch scheme is then employed to extract an estimate of the joint spectrum of noise free input-output data from the ARMA spectrum, which is used to estimate the transfer function. The parametric method exploits the ARMA structure to give consistent estimates of the system parameters. The performances of the algorithms are illustrated using the results obtained from a numerical simulation study.