Cluster tools, each of which consists of several single-wafer processing chambers and a wafer handling robot, have been increasingly used for diverse wafer fabrication processes. Processes such as some low pressure chemical vapor deposition processes require strict timing control. Unless a wafer processed at a chamber for such a process leaves the chamber within a specified time limit, the wafer is subject to quality problems due to residual gases and heat. We address the scheduling problem for such time-constrained dual-armed cluster tools that have diverse wafer flow patterns. We propose a systematic method of determining the schedulable process time range for which there exists a feasible schedule that satisfies the time constraints. We explain how to select the desirable process times within the schedulable process time range. We present a method of determining the tool operation schedule. For more flexible scheduling under the time constraints, we propose a modification of the conventional swap operation in order to allow wafer delay on a robot arm during a swap operation. We compare the performance of the new swap strategy with that of the conventional swap strategy.