The problem of a crack propagating steadily in Mode III along the interface of two bonded viscoelastic materials modeled as standard linear solids is investigated. The mathematical method consists of the application of a Fourier transform and the solution of simultaneous Wiener-Hopf equations. The results show that the variation of the stress intensity factor with crack propagation velocity may exhibit different domains of behavior depending upon the relative magnitude of the short and long-time wave speeds of each constituent. The accuracy of the method is checked by a comparison of the general results with special limiting cases.