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Opportunities for searches for axion-like particles (ALPs) coupling tophotons in $\mathrm{e}^+\mathrm{e}^-$ collisions at the Future CircularCollider (FCC-ee) and International Linear Collider (ILC) are investigated. Weperform a study of the photon-fusion production of ALPs decaying into twophotons, $\mathrm{e}^+\mathrm{e}^- \overset{\gamma \gamma}{\longrightarrow}\mathrm{e}^{+}\;a(\gamma \gamma)\;\mathrm{e}^{-}$, over the light-by-lightcontinuum background, for the planned FCC-ee and ILC center-of-mass energiesand integrated luminosities. An analysis of the feasibility measurements ispresented using parametrized simulations for two types of detectors. Upperlimits at 95% confidence level (CL) on the cross section for ALP production,$\sigma(\gamma \gamma \to a \to \gamma \gamma)$, and on the ALP-photon couplingare obtained over the $m_a \approx 0.1$--1000 GeV ALP mass range, and comparedto current and future collider searches. Production cross sections down to$\sigma(\gamma \gamma \to a \to \gamma \gamma) \approx 1$ fb (1 ab) will beprobed at $m_a\approx 1$ (300) GeV, corresponding to constraints on theaxion-photon coupling as low as $g_\mathrm{a\gamma \gamma} \approx2\cdot10^{-3}$ TeV$^{-1}$.

Searches for axion-like particles via $\gamma \gamma$ fusion at future $\mathrm{e}^+\mathrm{e}^-$ colliders