System identification under closed-loop conditions is very important especially for operating plants and open-loop unstable systems. Orthonormal Basis Filter (OBF) models have many advantages over classical linear models. In this study, identification schemes for the OBF based models which include explicit noise models from closed-loop data are presented. The schemes address two distinct aspects of closed-loop identification, namely, model development from closed-loop data for systems that are open-loop stable and open-loop unstable. The first scheme is based on the direct identification approach and it is capable of handling both open-loop stable and unstable closed-loop identification problems. The second scheme is based on the indirect identification approach known as the two-stage method. The proposed schemes are illustrated through simulation case studies.