  The existence of a new, photon-like, massive particle, the gamma' or dark
photon, is postulated in several extensions of the Standard Model. These models
are often advocated to explain some recent puzzling astrophysical observations,
as well as to solve the unsofar unexplained deviation between the measured and
calculated values of the muon anomaly. Dark photons can be produced at e+e-
colliders both in continuum events and in vector meson transitions and can
eventually decay into an electron-positron pair. For a proper choice of the
parameters of the theory, a $\gamma'$ can have a relatively long lifetime and
can therefore be observed as an e+e- vertex well separated by the primary
interaction point. This case is discussed in reference to very high luminosity
e+e- colliders either in construction or under study in several laboratories in
the world. It is shown that a search strategy based on the detection of
displaced vertices can be in principle very effective in covering a rather wide
and to date unexplored region of the theoretical parameters space.
