In this paper we discuss identification of codependent VAR and VEC models. Codependence of order q is given if a linear combination of autocorrelated variables eliminates the serial correlation after q lags. Importantly, maximum likelihood estimation and corresponding likelihood ratio testing are… only possible if the codependence restrictions can be uniquely imposed. However, our study reveals that codependent VAR and VEC models are not generally identified. Nevertheless, we show that one can guarantee identification in case of serial correlation common features, i.e. when q=0, and for a single vector generating codependence of order q=1.