This thesis describes the investigation into the use of visual servoing to keep an unmanned aerial vehicle (UA V) aligned with overhead electricity distribution lines, in order to use it to inspect them. The UAV would carry cameras in order to capture video footage showing the line's condition. Firstly, the current methods of inspecting overhead electricity distribution lines, line-walking and manned helicopters, are described. A review of visual servoing and the relevant tracking methods is presented. Then a mathematical model of a ducted-fan UAV is developed. Analysis of the image geometry is performed to show how movements of the UAV affect the positions that the overhead lines appear in the images from the UAV's camera. This analysis shows that it should be possible to estimate the UAV's position relative to the lines if two cameras, one pointing forward and one pointing backwards, are used. The design and construction of a laboratory test rig to perform experiments is described. Then the image processing method, based on the Hough transform, used to extract the overhead lines from the image is described followed by the development of a tracker, which makes use of fuzzy logic and a Kalman filter, to track the overhead lines from frame to frame. Experiments are performed to see how well the UAV is able to follow the lines using the laboratory test rig. Finally, conclusions are drawn as to how well the system works as well as suggestions for the future direction of the project.