The dynamical behavior of chemical processes in the complex domain is studied. It is shown that both dynamically stable real-valued and dynamically stable complex-valued steady states can exist and that the existence of stable complex-valued steady states is a simple consequence of the bifurcation of a pair of real-valued solutions into the complex domain. Moreover, it is shown that typical process model equations such as mass and energy balances, equilibrium equations, and others can be easily integrated in the complex domain and that complex domain integration can correctly handle both time evolution across phase boundaries and situations in which the specifications of the final state are infeasible. Examples for a flash process for natural gas containing small impurities at conditions in the retrograde region and a variety of geometric illustrations are used to illustrate salient points.