Cross efficiency evaluation in data envelopment analysis (DEA) is an effective tool for ranking the performance of decision-making units (DMUs). Numerous cross efficiency evaluations have been proposed with different secondary goals using both peer-evaluation and self-evaluation. The neutral cross efficiency evaluation is an important secondary goal in the classical black-boxes DEA models; that is, the internal processes of the DMUs are often ignored in the efficiency evaluation. This study extends the idea of neutral cross evaluation to measure the efficiency of the basic two stage network systems and proposes a new neutral cross efficiency model. The proposed model is able to rank DMUs in sub-stages and decompose the cross efficiency measure of the system into the product of those of the stages. The results from two real-world examples show that the neutral cross efficiency model proposed in this paper can increase the discriminating power of a two-stage system and their sub-stages and can obtain more realistic weight scheme than basic two stage DEA model. (C) 2019 Elsevier Ltd. All rights reserved.