Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks. •We investigate two-stage DEA models with undesirable input-intermediate-outputs.•We use the free-disposal axioms to construct production possibility sets. We construct two-stage network DEA models with undesirable indexes.•The new approach is applied to evaluate the efficiencies of China׳s listed banks.