A Texture's properties can be animated by clicking the Current Time radio button in the Edit At area at the top of the texture's dialog. The Edit At controls are discussed briefly in the User Guide on page 131.
This works fine Brian, thank you. But I've got 50 identical objects in the scene and they don't change color simultaneously. Do I need to create 50 textures and animate them separately?
Do each of the 50 objects share a common Texture or do they each have their own Textures? Since you are animating the Texture itself the animation will show on any object that Texture has been applied to. If you have multiple objects with individual Textures, each Texture will have to be animated individually.
Rereading your question it appears that you have replicated 50 copies of a single object so they are all sharing the same Texture? In that case the texture animation should be happening simultaneously. Send me a copy of your model and I'll take a look at it.