SUMMARY The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FA1 media simplifies considerably these equations. In the FA1 medium, the density normalized elastic parameters uZlkl(x,) can be described by the relation urlkl(x,) = f2(x,)A,,kl, where are constants, independent of coordinates x,, and f2(xz) is a continuous smooth function of x,. The types of anisotropy (A,,kl) and inhomogeneity [f(x,)] are not restricted. The traveltime perturbations of individual seismic body waves (qP, qS1 and 4.92) propagating in the FA1 medium depend, of course, both on the structural pertubations [6f2(xz)J and on the anisotropy perturbations (6A+/), but both these effects are fully separated. The perturbation equations for the time delay between the two @-waves propagating in the FA1 medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations 6f2(x,) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split @-waves in inhomogeneous anisotropic media. Numerical examples are presented.