Most real-life production processes are multi-stage in nature. Characterization of such processes via concepts such as technical efficiency is considered important to firm managers for the stage-specific analysis of their business decisions in improving their performance. Therefore, it is imperative to estimate the efficiency of a firm not only for the network production system but also for its sub-processes to locate the sources of inefficiency. In this chapter, we deal with production processes characterized by a two-stage network structure that links their stage-specific processes with intermediate products (measures). In this two-stage production process, the first stage uses input resources to produce intermediate products, which are all, in turn, used as inputs in the second stage to produce final outputs.