An analysis is made of Love-wave propagation in a medium composed of transversely isotropic layers. This is the kind of anisotropy which most commonly occurs at the surface of the earth, and in particular is displayed by bedded sediments. The exact boundary value problem is solved for a simple layer and extended to multilayered media by a generalization of Haskell's technique. By a suitable redefinition of parameters, it is possible to cast the anisotropic problem into isotropic form so that existing programs, tables, and graphs can be used to determine the structure of layered anisotropic media. It can be shown that the Love-wave period equation expresses the condition of constructive interference between multireflected SH waves with directionally dependent velocities. Also, it is demonstrated analytically and numerically that a restricted form of the anisotropy considered here is the limit of a finely laminated solid as the laminations become much smaller than a wave length. For long wave lengths, a multilayered structure may be replaced by an equivalent single layer.