Recently, a 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 μ m on electrons. Such a photon collider covers the range of invariant masses W γ γ < 12 Ge V / c 2 . The physics program includes spectroscopy of C -even resonances ( c -, b -quarkonia, 4-quark states, glueballs) in various 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 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 Γ γ γ ( W ) are obtained at which resonances can be detected at a 5 σ confidence level in 1 year of operation.