  As any e$^+$e$^-$ scattering process can be accompanied by a hard photon
emission from the initial state radiation, the analysis of the energy spectrum
and angular distributions of those photons can be used to search for hard
processes with an invisible final state. Thus high energy e$^+$e$^-$ colliders
offer a unique possibility for the most general search of Dark matter based on
the mono-photon signature.
  We consider production of DM particles via a mediator at the International
Linear Collider (ILC) and Compact Linear Collider (CLIC) experiments taking
into account detector effects within the DELPHES fast simulation framework.
Limits on the light DM production in a generic model are set for a wide range
of mediator masses and widths. For mediator masses up to the centre-of-mass
energy of the collider, results from the mono-photon analysis are more
stringent than the limits expected from direct resonance searches in Standard
Model decay channels.
