We investigate the influence of thermostatting methods on the electrical conductivity and structure of molten and supercritical sodium chloride obtained in nonequilibrium molecular dynamics simulations in strong constant (dc) electric fields. The strong dependence of the results on the type of thermostat employed in simulations becomes apparent only at extremely high fields (>0.5 x 10(9) V/m). For this range of fields, quantitative differences of unexpected size can be seen in the melt. In the supercritical fluid, different thermostats predict qualitatively very different behavior and structure. While the kinetic-type thermostats predict increased association of ions in the field, configurational thermostat predicts enhanced dissociation. (C) 2003 American Institute of Physics.