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The integrity of the brain's white matter is important for neural processing and displays age-related differences, but the contribution of changes in white matter to cognitive aging is unclear. We used latent change modeling to investigate this issue in a sample of very old adults (aged 81-103. years) assessed twice with a retest interval of 2.3. years. Using diffusion-tensor imaging, we probed white matter microstructure by quantifying mean fractional anisotropy and mean diffusivity of six major white matter tracts. Measures of perceptual speed, episodic memory, letter fluency, category fluency, and semantic memory were collected. Across time, alterations of white matter microstructure in the corticospinal tract were associated with decreases of perceptual speed. This association remained significant after statistically controlling for changes in white matter microstructure in the entire brain, in the other demarcated tracts, and in the other cognitive abilities. Changes in brain volume also did not account for the association. We conclude that white matter microstructure is a potent correlate of changes in sensorimotor aspects of behavior in very old age, but that it is unclear whether its impact extends to higher-order cognition.