  The next generation electron-positron colliders are designed for precision
studies of the Standard Model and its extensions, in particular in the Higgs
sector. We consider the potential for discovery of composite Higgs models in
Higgs pair production through photon collisions. This process is
loop-generated, thus it provides access to all Higgs couplings and can show new
physics effects in polarized and unpolarized cross-sections starting at
relatively low collider energies. It is, therefore, relevant for all
electron-positron colliders planned or in preparation. Sizeable deviations from
the Standard Model predictions are present in a general class of composite
Higgs models, as couplings of one or more Higgs bosons to fermions, or
fermionic and scalar resonances, modify the destructive interference present in
the Standard Model. In particular, large effects are due to the new quartic
coupling of the Higgs to tops and to the presence of a light scalar resonance.
