The authors develop a notion of axis in the Culler-Vogtmann outer space $mathcal_r$ of a finite rank free group $F_r$, with respect to the action of a nongeometric, fully irreducible outer automorphism $phi$. Unlike the situation of a loxodromic isometry acting on hyperbolic space, or a pseudo-Anosov mapping class acting on Teichmuller space, $mathcal_r$ has no natural metric, and $phi$ seems not to have a single natural axis. Instead these axes for $phi$, while not unique, fit into an ""axis bundle"" $mathcal_phi$ with nice topological properties: $mathcal_phi$ is a closed...