A process and apparatus for sampling a serial digital signal (D), which includes phasing of the digital signal with a clock signal (C) and sampling the digital signal at delayed instants (Si), wherein the phasing is carried out in reference to the sampling instants. The phasing includes determining phasing test instants (Pi) which refer to the sampling instants (Si) to verify whether transitions of the digital signal are leading or lagging in phase relative to the phasing test instants. The determination of the phasing test instants is achieved by adding to each sampling instant (Si) a delay Y=kR/2, in which k is a positive whole odd number other than zero and R designates a pulse repetition period of the bits of the digital signal (D). The invention has particular utility in data processing and remote data processing systems, and to telecommunication systems.