We discuss the construction of computational superstructures enabling time-dependent process simulation codes to perform stability. continuation and bifurcation calculations-tasks in principle not accessible to them-directly. The basis of the approach is the so-called Recursive Projection Method of Shroff and Keller (SIAM Journal of Numerical Analysis 31). We discuss its implementation and performance for the detection of different types of bifurcations (with emphasis on Hopf bifurcations) as well as slight modifications appropriate for index 1 partial differential/algebraic equations (PDAE) simulators. Tests that help discriminate between physical and numerical (spurious) bifurcations detected in the process are discussed and illustrated through the standard example of a tubular reactor with a single irreversible exothermic reaction. (C) 2003 Elsevier Science Ltd. All rights reserved.