Two basic neuroimaging-based characterizations of white matter tracts are the magnitude of water diffusion along the principal tract orientation (axial diffusivity, AD) and water diffusion perpendicular to the principal orientation (radial diffusivity, RD). It is generally accepted that decreases in AD reflect disorganization, damage, or loss of axons, whereas increases in RD are indicative of disruptions to the myelin sheath. Previous reports have detailed the heritability of individual AD and RD measures, but have not examined the extent to which the same or different genetic or environmental factors influence these two phenotypes (except for corpus callosum). We implemented bivariate twin analyses to examine the shared and independent genetic influences on AD and RD. In the Vietnam Era Twin Study of Aging, 393 men (mean age = 61.8 years, SD = 2.6) underwent diffusion-weighted magnetic resonance imaging. We derived fractional anisotropy (FA), mean diffusivity (MD), AD, and RD estimates for 11 major bilateral white matter tracts and the mid-hemispheric corpus callosum, forceps major, and forceps minor. Separately, AD and RD were each highly heritable. In about three-quarters of the tracts, genetic correlations between AD and RD were >.50 (median = .67) and showed both unique and common variance. Genetic variance of FA and MD were predominately explained by RD over AD. These findings are important for informing genetic association studies of axonal coherence/damage and myelination/demyelination. Thus, genetic studies would benefit from examining the shared and unique contributions of AD and RD.