We present a modular shock-fitting algorithm for unstructured grids that can be used in conjunction with virtually any vertex-centred shock-capturing solver. The unstructured, shock-fitting algorithm, originally developed for ideal gases, has here been extended to thermochemical nonequilibrium flows and coupled with COOLFluiD, an in-house shock-capturing CFD solver developed at the Von Karman Institute. Results obtained in the computation of hypersonic flows past circular cylinders are presented for both ideal gas and dissociating Nitrogen in thermochemical nonequilibrium