Given a legacy dynamic simulator of a chemical process plant, we construct a computational procedure that can be wrapped around the simulator to compute its steady states (both stable and unstable) and their dependence on input parameters. We apply this approach to the Tennessee Eastman (TE) challenge problem presented by Downs and Vogel, who also provided a FORTRAN process model. Using the FORTRAN simulator as a black-box input-output map, we enable it to systematically converge to isolated solutions and study their stability and parametric dependence within the equation-free framework. The presence of neutrally stable modes in TE problem (due to so-called inventories), their interplay with the problem formulation and the convergence of the solution procedure is explored and rationalized. Interestingly, our time-stepper formulation can automatically take advantage of separation of time scales, when present, to enhance computational convergence. The approach enables legacy dynamic simulators to calculate several dynamic problem characteristics useful for controller design and/or process optimization. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3308-3321, 2013