The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollowcylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal.