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Abstract Recently, a $$\gamma \gamma $$ γ γ collider based on the existing 17.5 GeV linac of the European XFEL has been proposed. High-energy photons will be generated by Compton scattering of laser photons with a wavelength of 0.5–1 $${\,\upmu \mathrm m}$$ μ m on electrons. Such a photon collider covers the range of invariant masses $$W_{\gamma \gamma } <12$$ W γ γ < 12 $${\mathrm {\,Ge V\!/}c^2}$$ Ge V / c 2 . The physics program includes spectroscopy of $$ C $$ C -even resonances (c-, b-quarkonia, 4-quark states, glueballs) in various $$J^P$$ J P states. Variable circular and linear polarizations will help in determining the quantum numbers. In this paper, we present a summary of measured and predicted two-photon widths of various resonances in the mass region 3–12 $${\mathrm {\,Ge V\!/}c^2}$$ Ge V / c 2 and investigate the experimental possibility of observing these heavy two-photon resonances under the conditions of a large multi-hadron background. Registration of all final particles is assumed. The minimum values of $$\varGamma _{\gamma \gamma }(W)$$ Γ γ γ ( W ) are obtained at which resonances can be detected at a $$5\sigma $$ 5 σ confidence level in 1 year of operation.