A clock signal generator comprising a first oscillator which normally supplies clock pulses to the output of the clock signal generator, a first counter for counting the pulses generated from the first oscillator and producing a carry signal after counting n1 pulses generated from the first oscillator, a second oscillator for producing clock pulses for possible back-up purpose, a second counter for counting the pulses generated from the second oscillator and adapted to produce a carry signal after counting n2 pulses generated from the second oscillator and to be reset by the carry signal from the first counter, n2 being larger than n1, and a control circuit which blocks the output from the second oscillator as long as no carry signal is supplied thereto from the second oscillator. Therefore, should the first oscillator fail to produce period pulses, the second counter is not reset any more and the control circuit stops blocking the pulses from the second oscillator and forwards them to the output of the clock signal generator. Thus, the clock signal generator can continue to supply clock pulses even when one of its oscillators should fail to operate properly, and the reliability of the clock signal generator is improved.