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We introduce the difficulties in processing context switches, exceptions, and interrupts in DMR architectures. We propose ways to address these problems in a dynamic DMR (DDMR) architecture, providing methods that assure both cores detect the event, synchronize it to the same instruction, perform a secure context switch, run correct interrupt service routines, and avoid process termination. DDMR uses a time-division multiplexing (TDM) ring architecture to dynamically connect pairs of cores. We enhance this protocol to include the different message types required to handle interrupts and exceptions. We also propose a more efficient address-based, rather than TDM-based, ring architecture.