  We state a condition for an observer to be comoving with another observer in
general relativity, based on the concept of lightlike simultaneity. Taking into
account this condition, we study relative velocities, Doppler effect and light
aberration. We obtain that comoving observers observe the same light ray with
the same frequency and direction, and so gravitational redshift effect is a
particular case of Doppler effect. We also define a distance between an
observer and the events that it observes, that coincides with the known affine
distance. We show that affine distance is a particular case of radar distance
in the Minkowski space-time and generalizes the proper radial distance in the
Schwarzschild space-time. Finally, we show that affine distance gives us a new
concept of distance in Robertson-Walker space-times, according to Hubble law.
