The zeroth- and first-order approximations for the eigenvalue Damköhler number are determined for the steady, one-dimensional isobaric adiabatic combustion of a fuel-lean gaseous premixture under a direct one-step Arrhenius-type exothermic chemical reaction in the physically interesting limit of (1) activation temperature large relative to the hot-boundary temperature; (2) (constant) Lewis-Semenov number of order unity; and (3) fuel and oxidant stoichiometric coefficients of order unity. It is shown that, to zeroth-order of approximation, the bimolecular system behaves as a monopropellant decomposition. The dependence on the parameters of the departure of this system from such behavior, to first-order of approximation, is established.