Abstract: The coupled-mode method based on the direct global matrix approach for acoustic propagation in rangedependent waveguides is numerically stable, accurate, efficient, and applicable to general range-dependent waveguide propagation problems. Luo el al. developed the direct-global-matrix coupled-mode model referred to as DGMCM (Luo et al., numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides, Sci. China-Phys. Mech. Astron. 55, 572(2012)). Compared to the coupled-mode model COUPLE, DGMCM has the following significant improvements:unconditional stability; more extensive applicability; improved efficiency. The model DGMCM has the same level of accuracy as the model COUPLE, and both of them can provide complete two-way solutions, resulting in higher accuracy over the one-way parabolic-equation model RAM. Differences between the models DGMCM, COUPLE, and RAM are analyzed, which are also verified by numerical examples.