A Coupled-Integral-Equations Technique (CIET) for the analysis of multiple discontinuities and bifurcations in rectangular waveguides is presented. A set of coupled integral equations for the tangential electric field over the planes of the discontinuities are derived and then solved by the moment method. Basis functions, which include the edge conditions and mirror images in the walls of the waveguide, are used to accelerate convergence of the numerical solution. One or two basis functions are sufficient to accurately determine the reflection and transmission properties of H-plane discontinuities and bifurcations. Reflection and transmission properties of N discontinuities are computed accurately from a single matrix of the order of 3N x 3N instead of cascading the individual generalized scattering matrices whose dimensions increase rapidly as the distances between the discontinuities decrease.