The existence of a new, photon-like, massive particle, the γ ′ 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 γ ′ 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