In multi-component reacting flows, it is well-known that significant simplifications are available when the "all-Lewis-numbers-are-unity" assumption can be justified. Under this assumption, certain linear combinations of the dependent variables, commonly known as the Shvab-Zel'dovich (SZ) variables, are "decoupled" from the chemistry terms. A derivation is presented here showing that the same simplifications can be achieved under less-restrictive conditions. The means to check whether these conditions are satisfied is provided. 0 2003 The Combustion Institute. All rights reserved.