This Thesis presents the development of an empirical and simple computer model for a voltage response of a ZnO element The derived model consists of a linear capacitor and atime-varying resistance. The data necessary for the derivation of the model is collected from testing on three ZnO elements with three different linear circuits. The front times of the voltage responses of the ZnO elements range from nanoseconds to submicroseconds. The front times of the current impulses being used to produce the voltage impulses varies from nanoseconds to microseconds. The voltages having nanosecond front times are measured with attenuators and the voltages with sub-microsecond-front time with a capacitor divider. Currents associated with the nanosecond-front-time voltages are measured with a technique founded on transmission line concepts. Currents associated with the submicrosecond-front-time voltages are obtained with a current shunt The response time of the capacitor divider and of the current shunt fall outside the ranges of the ratios of front time to response times specified in the IEC standard. Distortion introduced by the measuring devices into the measured signals is investigated with computer simulation. Conical transmission lines were constructed to test the voltage response of a toroidal ZnO element to the nanosecond-front-time current impulses. Analysis of the voltage response to the current impulses with sub-and-microsecond-front times indicates that at the beginning of the response, of a ZnO element it behaves as an approximately linear capacitor and subsequently as a capacitor in parallel with a timevarying resistance. The turn-on of the resistive behaviour occurs at approximately the first current peak The discrete voltage relating to the first current peak is named here the threshold voltage. This discrete voltage also denotes the tum-off of the resistive behaviour on the wave tail. The values of the apparent capacitances and permittivities of the ZnO elements are obtained. The apparent permittivities of the three ZnO elements are similar. The computed and measured variations of the resistance show good agreement The simulated and computed voltage responses of a ZnO element also show good agreement Atoroidal ZnO element is tested with the nanosecond-front-time current impulses. Analysis of the voltage response and the current-impulse shape by q-v curves and comparison of the measured responses to those of lumped linear capacitors show that a)the response of the ZnO element is capacitive and b) the capacitor characteristic is quasilinear. The simulated and computed voltage responses show good agreement The deviation from linearity originates from both the limited response of the attenuators and mismatches between the conical transmission lines and the section of the coaxial cable of the used current generator. The voltage response of miniature ZnO elements (also tested with the nanosecond-front time current impulses) show resistive behaviour. This Thesis also presents the design, construction and operation of a measuring system based on Rogowski coils. The model used for the analysis of the measuring system is an extended version of an existing model of a Rogowski coil. The model being introduced here can account for the interaction of the Rogowski coil with the remainder of the measuring system. This is applied successfully to the measurement of an impulse current flowing through a ZnO element