Disclosed are multiplex television signal processing apparatuses in a television signal transmitting and receiving system. An apparatus at the transmitting side comprises: a signal separator to separate a multiplex signal into a first and a second part; a time-multiplexer to time-multiplex a main television signal and the first part of the multiplex signal to obtain a time-multiplexed main signal; a first amplitude-modulator for modulating a first carrier by the multiplexed main signal to obtain a vestigial side band signal, amplitude-modulated main signal; a second amplitude-modulator for modulating a second carrier which is same in frequency as but different in phase by 90 degrees from the first carrier by a second multiplex signal; an inverse Nyquist filter for filtering this signal to obtain a vestigial side band, amplitude-modulated multiplex signal; and an adder for adding the vestigial side band, amplitude-modulated main and multiplex signals to obtain a multiplexed signal.An apparatus at the receiving side comprises: 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; a multiplex signal detector for detecting the first multiplex signal from the multiplexed signal passed through the filter by using the second carrier; a time-demultiplexer to time-demultiplexing the main signal into a main television signal and a second multiplex signal; and a signal composer for composing the first and second multiplex signal to obtain the original multiplex signal.