Steady quasi‐one‐dimensional flow is investigated for a general multi‐reaction system, for an arbitrary equation of state satisfying the Bethe‐Weyl conditions, and for a general class of lateral‐expansion specifications. The nature of the various solutions is investigated, particularly with reference to the approach to chemical equilibrium and to transonic flow, with a view toward establishing a correspondence between a downstream boundary condition, whether for a nozzle problem or a detonation, and various types of integral curve behavior. The question of unsupported detonation structure and the quasi‐one‐dimensional Chapman‐Jouguet condition is discussed and judged to be analogous to the one‐dimensional detonation problem. The frequently quoted Chapman‐Jouguet condition based on a special non‐equilibrium condition at a frozen‐sonic point is obtained only as a special case analogous to the “weak” one‐dimensional Chapman‐Jouguet condition. The equilibrium Chapman‐Jouguet condition based on equilibrium‐sonic flow is suggested as the normal case.