Reactivity-controlled compression ignition combustion has proved to be effective in reducing the pollutant emissions and the fuel consumption in four-stroke internal-combustion engines. The application of this combustion mode to portcontrolled crankcase-scavenged two-stroke engines also seems promising to avoid short-circuiting of fresh charge and to take advantage of the intrinsic residual exhaust gas. Accordingly, a computational study of a small-bore two-stroke dualfuel direct-injection reactivity-controlled compression ignition engine was made including computational fluid dynamics simulations and zero-dimensional modeling. The zero-dimensional model is used to supply suitable initial conditions for the computational fluid dynamics simulations and to generate useful operating maps. These maps predict the engine behavior, highlighting the conditions where combustion would be controllable by means of in-cylinder reactivity stratification. The computational fluid dynamics simulations were validated against experimental data under motored and fired conditions, and the spray model was calibrated against dedicated bench tests. The in-cylinder behavior was explored to understand the effect and the importance on the engine operation of several types of stratification, including thermal stratification and reactivity stratification caused by the scavenging process and fuel injections. The models emphasize the importance of the exhaust gas thermal content which can promote combustion. Furthermore, its stratification in the combustion chamber due to the scavenging process, together with the reactivity stratification caused by the dual-fuel injection is able to change both the combustion phasing and the combution duration, thereby increasing the efficiency and reducing the combustion roughness.