A multiplex signal processing apparatus in a signal transmitting and receiving system includes at the transmitting side: a first amplitude-modulator for modulating a first carrier by a main signal to obtain a vestigial sideband, amplitude-modulated main signal; a second amplitude-modulator for modulating a second carrier which has the same frequency but differs in phase by 90.degree. from the first carrier by a multiplex signal to obtain a double sideband, amplitude-modulated multiplex signal; an inverse Nyquist filter for filtering this signal to obtain a vestigial sideband, amplitude-modulated multiplex signal; and an adder for adding the vestigial sideband, amplitude-modulated main and multiplex signals to obtain a multiplexed signal. The apparatus at the receiving side includes: a Nyquist filter for filtering the multiplexed signal; a carrier regenerator for regenerating the first and second carriers from the multiplexed signal; a main signal detector for detecting the main signal from the multiplexed signal passed through the Nyquist filter by using the first carrier; a filter for removing quadrature distortion from the multiplexed signal; and a multiplex signal detector for detecting the multiplex signal from the multiplexed signal passed through the filter by using the second carrier. By inverse Nyquist filtering the auxiliary signal in quadrature to the picture carrier, a normal synchronous receiver will produce a conventional television signal without distortion (crosstalk) caused by quadrature distortion of an auxiliary signal containing additional picture information while at the same time allowing relatively simple demodulation of the auxiliary signal in improved receivers without adding distortion.