A relaxation oscillator system has a relaxation oscillator and a frequency control (FC) unit. The oscillator includes first and second oscillator sub-circuits and a latch. The first and second oscillator sub-circuits receive from the FC unit, respectively, first and second control signals for controlling corresponding outputs provided to the latch by the first and second oscillator sub-circuits. The latch outputs a variable frequency feedback signal provided to the FC unit. The FC unit receives a frequency control signal for controlling the frequency of an oscillator output signal and generates the first and second control inputs based on the frequency control signal and the feedback signal so that changes to the oscillator frequency are implemented by each oscillator sub-circuit while that sub-circuit is in an idle state to avoid glitches in the oscillator output signal.