An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates ω [subscript s] for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the ω [subscript s] are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions with transport equations for the basic components of which these species are composed. The second system retains the usual species transport equations, but eliminates the nonlinear algebraic equilibrium constraint conditions by deriving an explicit expression for the ω [subscript s]. Both systems are specialized to the case of an ideal gas mixture. Considerations involved in solving these equation systems numerically are discussed briefly.