Abstract: A hardware design emulation system that includes one or more emulators and one or more associated run-time assist units (RTAUs). The emulator logic is a combination of user model logic, reflecting the hardware design, and non-user model logic. A handshaking controller produces a domain step signal and a model step signal. The domain step signal indicates that the emulator is entering a state for executing the next step of the logic with which it is programmed, be it user model logic or non-user model logic. The model step signal indicates that the emulator is entering a state for advancing the user model defined by the user model logic. This dual handshaking protocol enhances versatility by enabling a wide variety of RTAUs to be used, particularly in combination with one another.