A theoretical account is given of methods of one- and two-dimensional electronic position encoding based on RC lines and resistive anode readout elements. The work was undertaken to support the development of imaging X-ray detectors for cosmic X-ray astronomy; other fields of possible application are noted. A brief review of imaging and non-imaging detectors used in X-ray astronomy is followed by a detailed account of the current generation of position-sensitive X-ray detectors and their associated readout elements. The standing of RC line and resistive anode readout in relation to other commonly-used systems is established. Quantitative descriptions of the non-linearity and resolution performance of capacitively-terminated RC lines using both amplitude ratio (charge division) and difference zero-cross time methods are given. The predictions of a series of calculations are compared with results from an extensive experimental programme. Optimum line configurations are defined. Calculations of the distortion and resolution performance of both square and circular resistive anode position encoders are presented. A numerical method is employed to solve the relevant potential problems in the limit of vanishing anode capacitance, allowing amplitude ratio methods to be examined in a number of electrode configurations. Analytical approximations permit the examination of two-dimensional zero-cross timing using resistive anodes. The properties of two alternative readout elements - Gear's anode and the four-quadrant anode - are discussed in relation to the performance of uniform resistive anodes. Finally, a possible application of the work reported here to the design of a future satellite experiment is discussed.