  Cosmological models with an SU(2) Yang-Mills field are studied. For a
specific model with a minimally coupled Yang-Mills Lagrangian, which includes
an arbitrary function of the second-order term and a fourth-order term, a
corresponding reconstruction program is proposed. It is shown that the model
with minimal coupling has no de Sitter solutions, for any nontrivial function
of the second-order term. To get de Sitter solutions, a gravitational model
with nonminimally coupled Yang-Mills fields is then investigated. It is shown
that the model with non-minimal coupling has in fact a de Sitter solution, even
in absence of the cosmological constant term.
