In semiconductor manufacturing, multicluster tools are widely employed for many wafer fabrication processes. With the demand for high-mix integrated circuit chips and shrinkage of circuit width, a scheme in which multiple wafer types are fabricated inside multicluster tools is adopted by wafer foundries to make more profits. Multiple wafer types, multiple robots, and wafer residency time constraints make the resulting scheduling problems challenging. This work focuses on scheduling a single-arm multicluster tool to process two wafer types concurrently subject to wafer residency time constraints in which a conventional one-wafer cycle and backward strategy are not efficient. With such properties, several necessary and sufficient conditions are presented to check the feasibility of a periodic schedule. Polynomial-time-complex algorithms are proposed to examine a tool's schedulability and coordinate multiple robots to handle wafers for schedulable scenarios. The cycle time of an obtained schedule can reach the lower bound. A practical example is used to show the effectiveness of the proposed algorithm.