This paper concerns subspace model identification of slowly time-varying systems operating in closed loop. Recursive MOESP-type closed loop subspace model identification algorithms are developed. The key technique of derivation of the proposed algorithms is the Hessenberg QR algorithm. Two forgetting mechanisms, namely, the exponential weight and the sliding data window, are introduced in order to track the time variation of the parameters of the systems. Numerical studies on a closed loop identification problem show the effectiveness of the proposed algorithms.