  The Higgs low-energy theorem gives a simple and elegant way to estimate the
couplings of the Higgs boson to massless gluons and photons induced by loops of
heavy particles. We extend this theorem to take into account possible nonlinear
Higgs interactions resulting from a strong dynamics at the origin of the
breaking of the electroweak symmetry. We show that, while it approximates with
an accuracy of order a few percents single Higgs production, it receives
corrections of order 50% for double Higgs production. A full one-loop
computation of the gg->hh cross section is explicitly performed in MCHM5, the
minimal composite Higgs model based on the SO(5)/SO(4) coset with the Standard
Model fermions embedded into the fundamental representation of SO(5). In
particular we take into account the contributions of all fermionic resonances,
which give sizeable (negative) corrections to the result obtained considering
only the Higgs nonlinearities. Constraints from electroweak precision and
flavor data on the top partners are analyzed in detail, as well as direct
searches at the LHC for these new fermions called to play a crucial role in the
electroweak symmetry breaking dynamics.
