Abstract-Waveform relaxation (WR) is a technique whichcan be used to solve large systems of ordinary differential equations (ODEs). It is especially suitable for the parallel solution of ODEs with multiple time scales, and has been successfully used for solution of electronic circuits and for solving partial differential equations (PDEs). The main issue limiting the utility of waveform relaxation is the class of problems with strong subsystem to subsystem couplings and long analysis time intervals resulting in non-uniform, slow convergence. Here we consider transmission line circuits since they represent an important part of a Spice type circuit solver. For transmission lines, the coupling between different lines is relatively weak, and thus partitioning in the transverse direction leads to very fast WR algorithms. However, longitudinal partitioning of transmission lines is very challenging due to the strong coupling which results. In this paper we propose an approach with improved convergence properties for strongly coupled longitudinal partitioning of transmission lines and other similarly strongly coupled circuits.Index Terms-Waveform relaxation and transmission lines, longitudinal partitioning, convergence analysis, fast convergence.