  Following previous works on generalized Abelian Proca theory, also called
vector Galileon, we investigate the massive extension of an SU(2) gauge theory,
i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian
vector Galileon. This particular symmetry group permits fruitful applications
in cosmology such as inflation driven by gauge fields. Our approach consists in
building, in an exhaustive way, all the Lagrangians containing up to six
contracted Lorentz indices. For this purpose, and after identifying by group
theoretical considerations all the independent Lagrangians which can be written
at these orders, we consider the only linear combinations propagating three
degrees of freedom and having healthy dynamics for their longitudinal mode,
i.e., whose pure St\"uckelberg contribution turns into the SU(2) multi-Galileon
dynamics. Finally, and after having considered the curved space-time expansion
of these Lagrangians, we discuss the form of the theory at all subsequent
orders.
