  We investigate homogeneous and isotropic cosmological solutions supported by
the SU(2) gauge field governed by the Born-Infeld lagrangian. In the framework
of the Friedmann-Robertson-Walker cosmology, with or without cosmological
constant $\lambda$, we derive dynamical systems that give rather complete
description of the space of solutions. For $\lambda=0$ the effective equation
of state $\ve(p)$ is shown to interpolate between $p=-\ve/3$ in the regime of
the strong field and $p=\ve/3$ for the weak field. Correspondingly, the
Universe starts with zero acceleration and gradually enters the decelerating
regime, asymptotically approaching the Tolman solution.
