While much attention has been given to nonlinear optical effects, there are also interesting effects on the shape of simple voltage transitions, in nonlinear transmission lines. Different portions of the wave front see different dielectric constants, and thus move with differing velocities, c/s/zie. This can cause self-steepening and shock formation. The detailed structure of the shock is determined by an equilibrium between the self-steepening action and the sources of dispersion of the system. If the spurious sources of dispersion can be minimized, then the steady state shock structure carries the “signature” of the dielectric dispersion. The shock structure is analyzed and its dependence on soft-mode frequency and soft-mode damping described. The shock can terminate in an oscillatory wake for wave fronts which are intense enough to give a strong nonlinearity in a material with an underdamped soft mode. © 1976, Taylor & Francis Group, LLC. All rights reserved.