Phase and group velocities are computed for several of the lowest modes of Love waves for a homogeneous spherical annulus overlying a homogeneous sphere. The solution is obtained by evaluating the contour integrals inpspace by a variety of asymptotic methods, each appropriate in a different range of frequency;pis the index of Bessel functions. Comparison is made with the corresponding solutions in a flat layer over a half‐space. Extension of the formalism is made to the case in which the inner sphere is inhomogeneou