Abstract: The continued-fraction algorithm can efficiently solve a scaled boundary finite element equation expressing the dynamic stiffness over an unbounded domain, and has a large convergence range and a high convergence rate. In this paper, a doubly asymptotic continued-fraction algorithm based on the singly asymptotic approach is developed to solve vector wave equations; the algorithm rapidly converges to the exact solution over the whole frequency range with increasing order of expansion. The factor matrices X⁽ⁱ⁾ are introduced to the continued fraction solution to improve the numerical stability of the solution. The coefficients of the solution are determined recursively by satisfying the scaled boundary finite element equation for dynamic stiffness at both the high and low frequency limits. The solutions for a 2-D semi-infinite wedge and a 3-D homogeneous half space are presented as examples. The results of these two examples demonstrate that the doubly asymptotic algorithm is more stable than and superior to the singly asymptotic approach.