A novel, flux-based, directed relation graph (DRG) method is proposed for adaptive and automatic generation of skeletal chemical mechanisms. Unlike many previous approaches for static mechanism reduction, the proposed method does not rely on the complete solution of a set of test problems using the detailed mechanism, but rather it simplifies the model "on the fly," analyzing the local reaction states with an extended directed relation graph. Compared to the original DRG method of Lu and Law [T. Lu, C.K. Law, Proc. Combust. Inst. 30 (2005)], the flux-based DRG explicitly considers the effect of transport fluxes, as they provide a way to quantify the coupling of the governing equations among adjacent grid cells. The resulting numerical scheme operates on a cell-by-cell basis, so that different chemical submodels are applied in different regions of the flame. This approach leads to very large reduction ratios, in which most of the flame structure is resolved using about 30% of the chemical species employed in the full mechanism, while a more detailed model that considers roughly 70-80% of the total species is used only at ignition. The flux-based DRG method has been employed in the two-dimensional simulation of axisymmetric coflow flames for a variety of fuels and chemical kinetic mechanisms (three steady flames and one oscillating flame), with a speedup factor of about 20 obtained for the largest problem - a JP-8 flame. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.