This paper studies system identification of ARMA models whose outputs are subject to finite-level quantization and random packet dropouts. Using the maximum likelihood criterion, we propose a recursive identification algorithm, which we show to be strongly consistent and asymptotically normal. We also propose a simple adaptive quantization scheme, which asymptotically achieves the minimum parameter estimation error covariance. The joint effect of finite-level quantization and random packet dropouts on identification accuracy are exactly quantified. The theoretical results are verified by simulations. (C) 2012 Elsevier Ltd. All rights reserved.