The Liapunov-Schmidt technique of classical bifurcation theory is used to spatially average the convection-diffusion-reaction (CDR) equations over smaller time/length scales to obtain low-dimensional two-mode models for describing mixing effects due to local diffusion, velocity gradients and reactions. For the cases of isothermal homogeneous tubular, loop/recycle and tank reactors, the two-mode models are described by a pair of coupled balance equations for the mixing-cup (C-m) and spatial average () concentrations. The global equation describes the variation of C-m with residence time (or position) in the reactor, while the local equation expresses the coupling between local diffusion, velocity gradients and reaction at the local scales, in terms of the difference between C-m and . It is shown that the two-mode models have many similarities with the classical two-phase models of heterogeneous catalytic reactors with the concept of transfer between phases being replaced by that of exchange between the two-modes. It is also shown that when the local Damkohler number (ratio of local diffusion to reaction time) is small, the solution of two-mode models approaches the exact solution of full CDR equations, while for fast reactions the two-mode models retain all the qualitative features of the latter. Examples are provided to illustrate the usefulness of these two-mode models in predicting micromixing effects on homogeneous reactions. (C) 2003 Elsevier Science Ltd. All rights reserved.