The interaction of a rarefaction wave with a gradual monotonic area enlargement of finite length in a duct is studied both analytically and numerically. An analytical quasisteady flow analysis is presented first, to obtain asymptotic solutions for the flow at late times, after all transient disturbances from the interaction process have subsided. Analytical results are presented and discussed for the boundary between the two possible predicted asymptotic wave patterns and the corresponding asymptotic strengths of the transmitted, reflected, and other waves, as a function of both the incident rarefaction-wave strength and area-enlargement ratio, for perfect diatomic gases and air. Finally, numerical results obtained using the random-choice method are presented and discussed for the complete nonstationary rarefaction-wave interaction with the area enlargement. These results show clearly how the transmitted, reflected, and other waves develop and evolve with time, until they eventually attain constant strengths, in agreement with the quasisteady flow predictions for the asymptotic wave patterns.