The present work studies the flow and flame characteristics in the supersonic combustor of a dual-combustion ramjet engine. Numerical simulations are performed under both chemically-frozen and reacting conditions. The composition and temperature of the hot reactive mixture from the subsonic combustor (i.e. gas generator) are determined at three nominal equivalence ratios, 1.0, 2.0, and 3.0. Special attention is placed on the detailed flow evolution immediately downstream of the gas-generator exit, where complicate shock structures appear, and the compressible mixing layer is initiated. The mixture from the gas generator and the airflow from the isolator behave as under-expanded supersonic jets as they enter the supersonic combustor, creating expansion fans in the immediate downstream. The resultant overexpansion then induces oblique shock waves that reflect on the wall, the separated shear layers, or the Mach disks, leading to secondary shear layers. Behind the gas-generator exit nozzle rim that measures 2.7 cm in thickness, a recirculation zone is formed between two major shear layers that originate from the two incoming streams. The compressible mixing layer starts as these two shear layers merge at the tip of the recirculation zone. A distinctive “shock train” is observed, for the first time, between the inner shear layer and a secondary shear layer behind a Mach disk. After the chemically-frozen flows have achieved their steady state, chemical kinetics are activated. Since the rim of the gas-generator exit nozzle is large enough for the local flow residence time to be commensurate with the ignition delay time, stable combustion is established in the recirculation zone and spreads over the entire mixing layer. Two parameters are then proposed to measure the combustion completeness.