In a phase-locked circuit which is operable in response to an input complex signal to produce an output complex signal, a first complex multiplication is carried out between the input and the output complex signals to obtain a phase difference therebetween which appears as a complex phase difference. The complex phase difference is composed of a real part and an imaginary part which are individually allowed to pass through a low pass filter and to be supplied to a numerically controlled oscillator as a control signal. The control signal includes a frequency component even when the phase-locked circuit is put into an asynchronous state. The low pass filter may be replaced by a digital circuit comprising phase dividers.