One of the important goals of the proposed future e$^+$e$^-$ collider experiments is the search for dark matter (DM) particles using different experimental approaches. The most general one is based on the mono-photon signature, which is expected when production of the invisible final state is accompanied by a hard photon from initial state radiation. Reviewed in this contribution are recent results on the sensitivity to DM pair production of the International Linear Collider (ILC) which is under consideration to be built in Japan and Compact Linear Collider (CLIC) at CERN.

The ILC design is based on the technology of superconducting
accelerating cavities which allows to reach centre-of-mass energies of up to 500 GeV with a footprint of 31 km. The baseline design includes polarisation for both e$^-$ and e$^+$ beams, of 80% and 30%, respectively. At 500 GeV, ILC is expected to deliver the integrated luminosities of about 4 ab$^{-1}$.

CLIC is based on the two-beam acceleration scheme which, with an RF gradient of 100 MV/m, should allow to reach 3 TeV centre-of-mass energy at the final construction stage. Only the electron beam polarisation is included in the CLIC baseline design and an integrated luminosities of 5 ab$^{-1}$ is expected at 3 TeV.

Expected exclusion limits are presented for DM pair-production at
500 GeV ILC and at 3 TeV CLIC, for scenarios assuming heavy mediator exchange, as well as for light mediator scenarios, when very small mediator coupling to SM particles is assumed.