Rate-controlled constrained equilibrium provides a sound framework for deriving and testing low-dimensional models of combustion chemistry, yet its application so far has been limited. The purpose of this paper is twofold: to propose a formulation of RCCE as a differential-algebraic problem and show how existing formulations such as the constraint potentials can be derived from it, and to demonstrate how combustion problems involving flow, such as nonpremixed laminar flames, can be solved with RCCE. A 9-constraint set is employed to reduce a 63-species detailed mechanism for CH4-air combustion and is found to be sufficient for fairly accurate predictions of both ignition in a homogeneous reactor and the structure of nonpremixed laminar flames for a variety of strain rates, while the main features of the latter. can also be reproduced with a 7-constraint subset. (c) 2005 Published by Elsevier Inc. on behalf of The Combustion Institute.