  We consider the strong dynamics associated with a composite Higgs model that
simultaneously produces dynamical axions and solves the strong CP problem. The
strong dynamics arises from a new $Sp$ or $SU(4)$ hypercolor gauge group
containing QCD colored hyperfermions that confines at a high scale. The
hypercolor global symmetry is weakly gauged by the Standard Model electroweak
gauge group and an enlarged color group, $SU(N+3) \times SU(N)'$. When
hyperfermion condensates form, they not only lead to an $SU(5)/SO(5)$ composite
Higgs model but also spontaneously break the enlarged color group to $SU(3)_c
\times SU(N)_D$. At lower energies, the $SU(N)_D$ group confines, producing two
dynamical axions that eliminates all CP violation. Furthermore, small
instantons from the $SU(N)'$ group can enhance the axion mass, giving rise to
TeV scale axion masses that can be detected at collider experiments. Our model
provides a way to unify the composite Higgs with dynamical axions, without
introducing new elementary scalar fields, while also extending the range of
axion masses that addresses the strong CP problem.
