In this paper we indicate how techniques developed by Zimmer [8]regarding certain smooth actions of discrete groups on compact manifolds canbe extended to actions of discrete groups and semisimple Lie groups oncompact fiber bundles. The actions that we consider preserve a smooth volumedensity on the total space of the bundle that defines a smooth field ofvolume densities on the fibers. When the standard fiber has ‘low’ dimensionor the action preserves certain geometric structures on the fibers, Zimmer'stechniques can show that the action must be measurably conjugate to atopologically relatively isometric action.