Liang et al. (2008) [1] developed DEA models based upon game approach to decompose efficiency for two-stage network structures where all outputs of the first stage are the only inputs to the second stage. This paper extends Liang et al. (2008) [1] by assuming that the inputs to the second stage include both the outputs from the first stage and additional inputs to the second stage. Two models are proposed to evaluate the performance of this type general two-stage network structures. One is a nonlinear centralized model whose global optimal solutions can be estimated using a heuristic search procedure. The other is a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower. The newly developed models are applied to a case of regional R&D of China.