An integrated circuit receives a first and second clock signal and a select signal that selects one of the clock signals. A glitchless switching circuit supplies an output clock signal according to which of the first and second clocks is selected by the select signal. A reset circuit coupled to the glitchless switching circuit responds to a direction of a transition of the select signal and generates a first reset signal in response to a first direction of the transition and generates a second reset signal in response to a second direction of the transition. The reset pulses are supplied respectively to first and second paths in the glitchless switching circuit to reset the state machine formed by the first and second paths in the event one of the input clocks is absent.