A general theory of multi-response state-defining experiments for a multi-zone temporal analysis of products reactor, is developed using the Laplace transform and a generalization of the transfer matrix formalism previously introduced for single-response experiments. The theory provides a unified approach to multi-response modelling and an efficient means to compute the actual profiles of gases and surface species concentration in the reactor, as well as the values of the outlet fluxes numerically, using e.g. fast fourier transform. We investigate the kinetic/mathematical conditions under which explicit expressions for the moments of the outlet fluxes and series expansions for their transient values can be obtained. Several important examples are analyzed in detail, leading to simple criteria of instantaneousness for different reactants within a catalytic mechanism. In the case of thin-zone reactors, the criteria are significantly simplified, with equality (within experimental error) of "shifted residence times" of reactants being proposed as the criterion of instantaneousness. This is illustrated for the oxidation of propene on a vanadium oxide catalyst. (C) 2004 Elsevier Ltd. All rights reserved.