  Let $T$ be a torus and $B$ a compact $T-$manifold. Goresky, Kottwitz, and
MacPherson show in \cite{GKM} that if $B$ is (what was subsequently called) a
GKM manifold, then there exists a simple combinatorial description of the
equivariant cohomology ring $H_T^*(B)$ as a subring of $H_T^*(B^T)$. In this
paper we prove an analogue of this result for $T-$equivariant fiber bundles: we
show that if $M$ is a $T-$manifold and $\pi \colon M \to B$ a fiber bundle for
which $\pi$ intertwines the two $T-$actions, there is a simple combinatorial
description of $H_T^*(M)$ as a subring of $H_T^*(\pi^{-1}(B^T))$. Using this
result we obtain fiber bundle analogues of results of \cite{GHZ} on GKM theory
for homogeneous spaces.
