  Extensions of the Standard Model (SM) gauge group with a new $U(1)_X$ predict
an additional gauge boson. Through kinetic mixing with the SM photons featured
by a coupling $\epsilon$, the ensuing so-called dark photons $\gamma'$, which
acquire mass as a result of the breaking of the gauge group $U(1)_X$, can
interact with the SM field content. These massive dark photons can therefore
decay to pairs of leptons, hadrons, or quarks, depending on their mass
$m_{\gamma'}$. In this work, we discuss searches for dark photons in the mass
range around and below one GeV at the LHeC and FCC-he colliders. The signal is
given by the displaced decays of the long-lived dark photon into two charged
fermions. We discuss the impact of conceivable irreducible (SM and
machine-related) backgrounds and different signal efficiencies. Our estimates
show that the LHeC and FCC-he can test a domain that is complementary to other
present and planned experiments.
