Most modern chemical plants are complex networks of multiple interconnected nonlinear process units, often with multiple recycle and by-pass streams and energy integration. Interactions between process units open lead to plant-wide operability problems (i.e., difficulties in process control). Plant-wide operability analysis is often difficult due to the complexity and nonlinearity of the processes. This article provides a new framework of dynamic Operability analysis for plant-wide processes, based on the dissipativiry of each process unit and the topology of the process network. Based on the concept of dissipative systems, this approach can deal with nonlinear processes directly. Developed from a network perspective, the proposed framework is also inherently scalable and thus can be applied to large process networks. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 963-982, 2009