Abstract: The existing multi-stage DEA models are generally assumed that all inputs and outputs are desirable, few studies on the undesirable inputs and outputs and no study on undesirable initial inputs and intermediate outputs. Therefore firstly the method of defining the types of inputs and outputs is proposed, and it is applied to the two-stage system which includes undesirable inputs and undesirable outputs. And for the conditions of consistent and inconsistent of the same inputs or outputs' types especially intermediate outputs' types in two-stage production system with undesirable indicators, corresponding production possibility sets and two-stage DEA models are established. Finally, the proposed methods and models are used to evaluate the efficiency of China's listed banks.

Key words: undesirable inputs and undesirable outputs, two-stage system, production possibility set, DEA