Neuristor propagation analysis techniques apply to a wide variety of nonlinear distributed electronic devices and wave propagation phenomena. This paper brings together and reviews these techniques. A specific example, the superconductive tunnel junction stripline, is modeled by a distributed equivalent circuit described by nonlinear parabolic partial differential equations. The neuristor pulse propagates at constant velocity with a fixed waveshape; mathematically, this reduces the partial differential equations to ordinary differential equations which are solved by phase-plane topology analysis. Poincaré's index rule and Bendixson's negative criterion prescribe the pulse velocity and waveform. Analytical results agree with experiment. Pulse waveform stability is studied using eigenfunction expansion of the perturbation equations and Lyapunov theory, but complete results are not obtained. Lyapunov theory provides estimates of excitation thresholds for launching a neuristor pulse, which are consistent with experiment. Determining the nature of pulse interactions may for some systems be accomplished using the Bäcklund transformation or perturbation series techniques, but generally requires complete computer solution of the dynamical equations.