A systematic procedure based on the Liapunov-Schmidt method of bifurcation theory is used to derive low-dimensional models for different types of non-isothermal homogeneous, catalytic and coupled homogeneous-heterogeneous reactors. These low-dimensional models are described by multiple concentration and temperature modes (variables), each of which is representative of a physical scale of the system. These "multi-mode models" capture mass and thermal micromixing as exchange of material and energy, respectively, between the modes (scales). The multi-mode models retain all the parameters and most of the qualitative features of the full convection-diffusion-reaction equations. While in the limit of vanishingly small local heat and mass diffusion times, they reduce to the classical ideal pseudo-homogeneous reactor models, they are also capable of capturing the mixing or mass (and/or heat) transfer-limited asymptotes for the case of fast reactions. We illustrate the usefulness of the multi-mode models in predicting mixing and selectivity effects on reactor performance and the influence of local transport effects on reactor runaway and bifurcation behavior for the case of non-isothermal homogeneous and catalytic reactors. (C) 2004 Elsevier Ltd. All rights reserved.