A true random number generator (RNG) has one or more oscillators and an output register for storing a random number output. Each of the oscillators is activated, successively, in a free-running oscillation phase, and a capture phase during which the oscillator is quiescent. The output register latches during the capture phase of each oscillator an end state of that oscillator at or close to the end of its oscillation phase. The random number output is derived from the latched end states.