A theoretical 2-dimensional analysis is made of the end region of a single-load crossconnected m.h.d. generator in which the duct cross-section, fluid properties and magnetic field are uniform, infinitely fine segmentation of the crossconnected electrode system is assumed. With a single load connected between solid electrodes at each end of the generator, the analysis predicts infinitely high current densities and electric fields at the junction of the solid-electrode and crossconnected sections. it is shown that these infinite concentrations can be removed by using grading resistors near the ends, and the design of one arrangement of grading resistors is discussed.