ABSTRACT Flame propagation under thermal and compositional stratifications is relevant to a wide range of applications in combustion devices. In this work, numerical studies are conducted to investigate the multi-stage ignition process and flame propagation in the stratified methanol/n-heptane-air dual-fuel mixture under engine-like conditions. Firstly, the effects of the initial gas temperature of the oxidizer (TOX) and fuel stream on the ignition process and combustion modes are investigated. The results show that TOX affects the early-stage ignition, and a fuel-rich stabilization mode is observed at low temperatures. For example, at 800 K, both cool and hot flames are initiated at the regions close to the most reactive mixture fraction, . A transition from the fuel-lean to fuel-rich and then back to the fuel-lean regions in the mixture fraction space is observed at higher temperatures. Then, hot flames propagate into the methanol/air premixture, forming quasi-steady hot-flame fronts in the fuel-rich regions at TOX = 800 and 900 K owing to the lack of oxygen and low adiabatic flame temperatures. At 1000 K, another flame front propagates into the n-heptane/air mixtures owing to enhanced reaction rate at higher local temperatures. By increasing TOX, a balance owing to the gas expansion is observed at 1020 K, and a spontaneous ignition mode appears at temperatures above 1050 K owing to the high reactivity and early ignition of the methanol/air premixture. Secondly, the effect of compositional stratification on the ignition and flame structures is investigated. Compared with the double flame structure under thermal and compositional stratification conditions, only a single flame structure is observed for those cases with uniform temperatures. A high temperature in the fuel stream region accelerates the decomposition of n-heptane, resulting in the complete consumption of oxygen.