To satisfy the requirements of high-mix integrated-circuit chip production, multiple wafer types are grouped into a lot to be fabricated concurrently in a multi-cluster tool system. However, the existing studies do not solve the scheduling problem of multi-cluster tools with multiple wafer types being processed and wafer residency time constraints being imposed. This study aims to find a feasible steady-state schedule for a process-dominant multi-cluster tool that processes two wafer types concurrently. A novel robot cycle, called one-wafer-per-type cycle, and a two-swap robot sequence are defined, under which the minimal cycle time can be achieved. Further, the schedulability for individual cluster tools with two wafer types is proved upon closed-form derivations. The schedulability conditions of a one-wafer-per-type schedule for the system are proposed. With such conditions, an efficient algorithm is established to obtain a schedule in a two-swap sequence. Several instances show the application and effectiveness of the proposed method.